UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Passenger distribution functions for small airports 1984

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1984_A7 G43.pdf
UBC_1984_A7 G43.pdf [ 10.48MB ]
UBC_1984_A7 G43.pdf
Metadata
JSON: 1.0062964.json
JSON-LD: 1.0062964+ld.json
RDF/XML (Pretty): 1.0062964.xml
RDF/JSON: 1.0062964+rdf.json
Turtle: 1.0062964+rdf-turtle.txt
N-Triples: 1.0062964+rdf-ntriples.txt
Citation
1.0062964.ris

Full Text

PASSENGER DISTRIBUTION FUNCTIONS FOR SMALL AIRPORTS by ERICA GEDDES B.Sc, Queen's University, 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in FACULTY OF APPLIED SCIENCE DEPARTMENT OF CIVIL ENGINEERING We accept this thesis as conforming to the required standard > THE UNIVERSITY OF BRITISH COLUMBIA April 1984 © Erica Geddes, 1984 i In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements fo r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I further agree that permission f o r extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 (3/81) ABSTRACT This research looks at one input required for the design and planning of small airports. It investigates the number of passengers expected to use the terminal. Data describing passenger volumes was gathered from a i r l i n e flight records at eight airports in British Columbia. The volumes were formed into frequency distributions and a theoretical model was found that would best describe the data. The selection of the model was based on the overall f i t of the curve (as measured by the Chi-Squared s t a t i s t i c and by visual inspection) and the a b i l i t y of the model to predict the right hand t a i l of the observed curve (as measured by the 90th percentile values). Three model distributions were studied: the Normal, the Poisson and the Lognormal. According to the selection c r i t e r i a , the lognormal distribution was found to be the best model for use in a i r terminal design. i i i TABLE OF CONTENTS ABSTRACT i i LIST OF FIGURES v LIST OF TABLES v i ACKNOWLEDGEMENTS v i i 1. INTRODUCTION 1 1.1 Statement of Problem 1 1.2 Approach 2 2. LITERATURE REVIEW 6 2.1 Air Terminal Sizing 6 2.2 Design Volume Determination 17 2.3 Passenger Distribution Functions 19 3. METHODOLOGY 21 3.1 Data Description 21 3.2 Features of the Distributions 23 3.3 Procedure 27 3.3.1 Goodness-of-Fit Criterion 30 3.3.2 Design Volume Criterion 31 3.3.3 Visual Inspection Criterion 34 4. ANALYSIS 35 4.1 Criteria for Acceptance or Rejection 35 4.1.1 Goodness-of-FIt 35 4.1.2 Design Volumes 46 4.1.3 Visual Inspection 50 4.1.4 Ease of Use 53 4.1.5 Applicability 54 4.2 Selection of a Model 54 i v 5. CONCLUSIONS 56 5.1 Assessment 56 5.2 Further Research 58 REFERENCES 60 APPENDIX A - Computer Programs 63 APPENDIX B - Detailed Chi-Squared Calculations 69 APPENDIX C - Actual Deciles by F l i g h t Event 76 APPENDIX D - Histograms 79 V LIST OF FIGURES 1. Airport Terminal Passenger Flows 7 2. Terminal Planning Process 8 3. Terminal F a c i l i t i e s 10 4. 90th Percentile by Flight Event and by Passenger Volume 33 LIST OF TABLES v i I. Distribution Models Used by Airlines and Aircraft Manufacturers 5 II. Quantity of Available Data 22 III. Data Desception for Flights 24 IV. Data Description for Airports 25 V. Comparison of Calculated and C r i t i c a l Chi-Squared Values for Flights 37 VI. Comparison of Calculated and C r i t i c a l Chi-Squared Values for Airports 40 VII. Acceptance Rate by Flight 43 VIII. Acceptance Rate by Airport ( A l l Airports) 44 IX. Acceptance Rate by Airport (Airports with Multiple Flights Only) 45 X. Comparison of Actual and Predicted 90th Percentiles for Flights 47 XI. Comparison of Actual and Predicted 90th Percentiles for Airports 48 XII. Average Differences between Actual and Predicted 90th Percentiles 49 XIII. Visual Inspection of Histograms for Flights 51 XIV. Visual Inspection of Histograms for Airports 52 ACKNOWLEDGEMENTS I wish to express my thanks to Professor G.R. Brown for his guidance throughout this thesis. I would also like to thank the Terminal Services staff of Transport Canada's Pacific Region Airports Branch who made the study possible. 1 1. INTRODUCTION 1.1 Statement of the Problem Expenditure for the design and construction of airport terminals i s considerable. Even though regional airports are not as large as the international and national airports they connect to, the amount of capital and time involved can s t i l l be significant. For example, the expansion of the air terminal complex at Castlegar, British Columbia is expected to cost approximately $6 million. Of this, $2.5 million w i l l be spent to enlarge and renovate the terminal building with Che remaining $3.5 million going to parking lot reconstruction, relocation of services and design fees. The planning of the project began in 1981 and completion is expected to be in 1987. The fact that the design and construction w i l l take six years illustrates the magnitude of the effort involved. The purpose of this study was to improve the input to the analytical processes of air terminal design. The particular input looked at was the number of passengers expected to occupy small terminals. Airline records of passengers enplaning and deplaning for each flight were used to determine the number of passengers expected. The study looked at the frequency distribution curves of the flight volumes. Knowledge of the shape of these distributions w i l l help the terminal design process. For example, a peak volume (such as the 90th percentile) can be calculated and used as a design criterion. Alternatively, the f u l l distribution can be used for simulation models which randomly sample from the expected values. With this more accurate representation of passenger occupancies, the terminal design w i l l be more efficient. 2 1 . 2 Approach Records of the number of passengers getting on and off of aircraft were collected from small regional airports. They were compiled into frequency distributions. A common s t a t i s t i c a l distribution model was then found which would adequately describe the actual data so that i t could be used for the design of terminals. When passenger volume data is used for terminal design, i t is typically in one of the following forms: ( 1 ) design hour volume of passengers; ( 2 ) design flight load; (3) distribution of expected passengers; (4) distribution of expected fli g h t loads; (5) design daily pattern of passenger volumes, or ( 6 ) design daily flight schedule. If the passenger volumes (and flight load volumes) are described by a model distribution, the values to be used for the terminal design can be better determined. In this work, the data used to determine expected passenger volumes at the terminal was flight load data. The individual observations are the number of deplaned and enplaned passengers of one fli g h t stop. In other words, each data point Is the sum of a l l of the passengers getting off of the airplane when i t arrives at the airport, and a l l those boarding the airplane as i t departs. These two movements w i l l be designated as one "flight event". A l l airports in the study have one arrival and one departure association with each event - that i s , the flight routes do not originate or terminate at these particular sites. 3 These airports have only a few major flight events daily, and for each, the arrival and departure occur within the space of a half-hour. For these reasons, the passenger volumes of a flig h t event are equivalent to half-hourly volumes. This simplifies the analysis since flight event volumes can be measured to directly determine design volumes for planning. The flight events are grouped together into years, such that a "fl i g h t " w i l l be defined as the total of a l l of the flig h t events that occur, at the same time of the day over the course of one year. This means there w i l l be 366 or less flight events i n one f l i g h t . Since the volumes of passengers involved in each flight event vary over the year, each flight w i l l have a certain distribution of the frequency of occurrence of the flight volumes. To derive hourly planning volumes, however, a l l hours with activity must be compiled for the year. Therefore, as a second step, a l l events of a l l flights at an airport w i l l be combined to form another frequency distribution. This, then, w i l l be the data under study - individual flights and flights compiled at each airport. Each distribution w i l l be formed into a histogram so that i t can be compared to theoretical s t a t i s t i c a l models. Originally, nine possible distribution models were considered: (1) Binomial (2) Polsson (3) Normal (4) Gamma or Erlang (5) Weibull (6) Lognormal 4 (7) Negative Binomial (8) 5th Degree Polynomial (9) Beta Of these, three were selected for further study: the Normal, Poisson and Lognormal. The three are relatively simple to understand, to calibrate, and to apply. They also appeared to reasonably represent the shape of the observed distributions. Table I shows some of the distributions used by airlines and aircraft manufacturers. Both quantitative and qualitative methods were used to select the distribution which would best replicate the actual data. A computer performed the most of quantitative work by doing two things. F i r s t , the Chi-squared s t a t i s t i c was calculated for each distribution model and compared to the theoretical Chi-squared values. This comparison determined i f the model provided a s t a t i s t i c a l l y significant f i t . The second application of the computer was to measure the a b i l i t y of each model to accurately predict the behaviour of the upper t a i l (the right hand end) of the distribution. This is particularly useful i n the determination of peak design volumes. Actual and predicted 90th percentile volumes were calculated to measure the t a i l behaviour. The third criterion used to evaluate the three models was more subjective. It involved visually inspecting each observed and expected histogram and ranking each model according to i t s a b i l i t y to reproduce the observed data. Finally, the selection of the best model was based on i t s a b i l i t y to be understood and to be applied. 5 TABLE I Distribution Models Used by Airlines and Aircraft Manufacturers Distribution Users Binomial Quantas (business and 1st classes) Polsson Normal United Airlines, Boeing, Lockheed, KLM, Quantas (economy class) Pan American, Air Canada Gamma/Erlang Swiss Air Weibull American (now switched to Rayleigh) Lognormal McDonnell-Douglas Negative Binomial British Airways 5th Degree Polynomial Lufthansa Beta (empirical model) Cathay Pacific Source: References - Lauehli 1 1*, Vella, et a l 2 2 ; Wang2<+; Soumis et al 6 2. LITERATURE REVIEW An airport terminal is a transfer point between ground and air transportation systems. By most definitions, the air terminal includes the building structure, the roadway curb, the station platform i f the airport is served by transit, and the aircraft apron. The flow between ground and air i s shown schematically In Figure 1. The purpose of the air terminal i s to aid this transfer between ground and air and also, in the case of connecting passengers, between air and air. Although the system of pedestrian movement is complex, the transfer must be done as quickly, as comfortably and as effic i e n t l y as possible. Planning an air terminal is a complicated and usually lengthy process. Careful design w i l l be even more c r i t i c a l as capital funds are reduced and a premium is placed on the space available. A typical framework for the planning process is given in Figure 2. There i s , at present, no universal procedure for the generation of terminal designs nor for the evaluation of proposed terminal concepts. This is not to say, of course, that methodologies do not exist. There are numerous ways to size f a c i l i t i e s and to model the movement of pedestrians between them. These w i l l be discussed below. 2.1 Air Terminal Sizing Planning of airport terminals incorporates the sizing of their f a c i l i t i e s and the arrangement of these f a c i l i t i e s within a building structure. Some of these elements are mandatory stops for passengers; others are optional. Essential for processing are the ticketing and bag 7 FIGURE 1 Airport Terminal Passenger Flows Arriving Departing APRON Deplaning Enplaning TERMINAL BUILDING Terminating Originating CURB AIRSIDE GROUNDSIDE V 8 FIGURE 2 Terminal Planning Process NEED IDENTIFIED AVIATION FORECASTS OPERATING POLICY FACILITY SIZING USER INPUT + FORECASTS OF COSTS AND REVENUES LAYOUT CONCEPTS GENERATED EVALUATION OF CONCEPTS OPTIMIZATION AND SELECTION OF CONCEPT • • check-in counters, security checkpoints, holdrooms, gates and baggage claim devices. Occasionally, some of these may be bypassed i f , for example, a passenger has no checked luggage or i f ticketing i s done on board the aircraft. Optional components vary from airport to airport. Some examples are restaurants, washrooms, telephones, giftshops and banks. Space is also provided for the offices of airline and airport employees as well as for electrical and mechanical u t i l i t i e s . F a c i l i t i e s can be further divided into those used by enplaners (ticketing, holdroom) and those used by deplaners (baggage claim). Figure 3 shows the basic passenger flow for a simple terminal layout. The function of terminal planners Is to balance the demands of passengers, airline companies, government agencies, concessionaires and other airport users with the services to be supplied by the f a c i l i t i e s . Obviously, the objectives of these parties w i l l often conflict. There are, however, three tenets that are geneally accepted as being fundamental to good design - that the terminal be flexible, economic, and provide an acceptable level of service to the users. Some facets of each of these are: ( 1 ) F l e x i b i l i t y to allow for: - staged growth - new technology - unforeseen circumstances 10 FIGURE 3 Terminal F a c i l i t i e s H0LDR00M SECURITY GENERAL WAITING AREA CONCESSIONS/SERVICES AIRLINE OFFICES/ CARGO AREA TICKETING/ CHECK-IN DEPLANING/ ARRIVING PASSENGERS ENPLANING/ DEPARTING PASSENGERS 11 (2) Economic Optimization of: - capital costs - operations and maintenance costs - revenues - benefits to users (often intangible) (3) Level of Service as Affected by: - area per person - waiting times - walking distances (inside and outside; with and without bags) - temperature and humidity - lighting - amenities (such as seating, no-smoking areas) - concessions - handling of disabled persons - information systems In most terminal design methods, the space required for each function i s calculated on the basis of an expected peak occupancy. The occupants are each allotted a certain area, the amount of which is dependent upon the purpose of the area and upon some measure of personal comfort. The latter is quantified into discrete categories known as Levels of Service. For example, at a given Level of Service each person in the general waiting area may be given 1.5 square metres of space but the occupants of the holdroom would be deemed to need only 1.0 square metre. For a reduced Level of Service, these areas would be, say, 1.2 and 0.7 square metres respectively. 12 The design occupancy is either determined directly from a design volume or is calculated by a model of the terminal flows. In the former case, the number of passengers in the area i s taken as a proportion of a design flight volume, or of the airport's peak hourly design volume. The proportion is based on historical patterns. If greeters and well-wishers are permitted in the f a c i l i t y , the ratio of non-passengers to passengers is multiplied by the number of passengers to find the total occupancy. This method of fixed proportions was used extensively by Transport Canada u n t i l a few years ago. It i s the simplest way of calculating f a c i l i t y space requirements, aside from using standard terminal layouts. For this reason i t is s t i l l used, both in Canada and the United States, when more advanced tools are unavailable or for preliminary estimates. There are d i f f i c u l t i e s , however, with the use of typical proportions of design volumes. De Neufville® explains this as being due to the method not incorporating the stochastic features of the movements through the terminal. Models which incorporate pedestrian flows are better able to predict the dynamic nature. They can also point out c r i t i c a l areas of congestion (often the ticketing area and the bag claim area). Flow models are typically used to evaluate proposed layouts. They do not generate layouts, which i s a largely subjective process, although attempts have been made to quantify i t . For example, Braaksma and Ramsey5 developed two indices to catalogue terminal layouts. Braaksma also developed 3 a computerized method of creating preliminary layouts. There are basically four categories of analytical methods for analyzing terminal flows (based on Horonjeff 1 2): 13 (1) Network Models Network models ill u s t r a t e the airport functions and describe their Interrelationship in the processing system. Once the processing times of each link and the passengers' paths through the network are known, the total trip time can be estimated. Analysis of the network can identify c r i t i c a l links that affect the entire system. Braaksma applied a CPM network model to evaluate passenger delay (Simulating the Turnaround Operation of Passenger Airfract using the C r i t i c a l Path Method, University of Waterloo, 1970). This approach does not consider the volume of passengers travelling on any link or path. It does not assign passengers to paths, predict the effects of queue building nor model random behaviour. (2) Queueing Models Entrance and exit queueing models can be developed for each f a c i l i t y . Standard formulae can not be used because the demand is not steady, but builds up and dissipates with each f l i g h t . The f a c i l i t i e s have to be analyzed in the order in which passengers go through them. For example, an analysis of the ticket counter could use a cumulative distribution curve of passenger arrival times and the average service rate of the ticketing agents. Both would be plotted. The queue length and waiting times would then be determined graphically from the differences in the curve. (Queueing models are well-explained by Horonjeff* 2 and de Neufvllle 8). Ashford and Wright 1 describe the d i f f i c u l t y with these models when several f a c i l i t i e s are linked together in chains: the mathematics may become lntactable when random arrivals and exponential service times are incorporated. ( 3 ) Simulation Models These aire computer models which can provide very detailed information, but can be expensive to run. By definition their inner workings cannot be explained by simple equations and so can be d i f f i c u l t to validate. An example is the Vancouver Airport Simulation Model 2 1 . Simulation models operate on a projected flight schedule. Passenger arrival ratio, processing rates, walking speeds and passenger routes are also input the variables may be fixed, or the model may randomly select them from a distribution. By iteration, the movement of a l l persons throughout the day are found producing computations of delays, transit time, and occupancies. ( 4 ) Hydraullc/Hydrologic Models This i s a relatively new type of model for terminals which assumes pedestrians behave in a manner similar to f l u i d flow. Ramsey and Hutchison^ used a flood flow analogy and found i t less expensive than the Vancouver Airport Simulation Model. Their model routes passengers through the system in the way i n which a storm proceeds through the various reaches of a river. As input, a daily schedule is required which initiates the "storms" of passengers and determines the volume of passengers flowing through the terminal. Resistance characteristics of the processors and links as well as the desired level of service are also required model inputs. There are obvious benefits to the use of these models. Once set-up, they can be repeated in order to evaluate proposed layouts and to examine their sensitivity to variations in input. They can model the entire system or only a part of i t . 15 Like a l l analytical methods, terminal models are only as useful as the information input into them, which typically includes: ( 1 ) characteristics of passengers, non-passengers and baggage; (2) aircraft types and characteristics; ( 3 ) activity levels of passengers and aircraft; ( 4 ) rates of arrival, usually in relation to flight times; ( 5 ) processing and flow rates; and ( 6 ) the variations of a l l of the above factors over the course of the day. This information may be d i f f i c u l t , i f not impossible to obtain. Survey information such as found by the extensive surveys done in the Canadian Airports System Evaluations 4, can be used for model input. Alternatively, a survey can be used directly to determine f a c i l i t y occupancy but since a survey can only be done for a few days, the results may not be representative. These are the usual methods of airport terminal sizing. As explained above, peak occupancies are determined from design volumes or from models. The areas are calculated by multiplying the number of occupants by a given unit area. Some iteration may be necessary since the size of an area w i l l affect the travel times through i t and, therefore, the flows. In an effort to simplify design Transport Canada is now using standard layouts for a l l new terminals. The process i s called the Systemized Terminal Expansion Program, or STEP 2 0. The purpose of the program is to avoid repetition of the design process since the requirements of small terminals tend to be similar. It also speeds the selection, review, and approval processes, as well as the preparation of the contract drawings. Furthermore, by incorporating a pre-planned expansion capability, 16 terminals are able to adjust to changing t r a f f i c conditions, which are often d i f f i c u l t to forecast at small sites. The design year for STEP buildings i s the year of opening, although the chosen size must suffice for three years. By minimizing the time to the design year, there is more certainty i n forecasting the requirements. The lifespan of three years was chosen to balance the added cost of expansion with the savings made by delaying the construction. Originally, the selection of a STEP terminal was based upon six c r i t e r i a : (1) Total Annual Passengers This i s an easily obtained s t a t i s t i c which gives a general Indication of the airport size. However, i t is too broad to be of use in f a c i l i t y sizing. (2) Planning Volume This hourly volume would more accurately reflect the demand made on the f a c i l i t i e s . It i s not yet o f f i c i a l l y defined for small airports, but the 90th percentile (of a l l hours with t r a f f i c ) has been used. Complete data is d i f f i c u l t to collect, however, for small airports. (3) C r i t i c a l Aircraft The largest scheduled aircraft also gives a reasonable idea of demand on the terminal. (In British Columbia, the c r i t i c a l aircraft is usually the Boeing 737). (A) Daily Movements of C r i t i c a l Aircraft This also provides an effective demand measure. 17 (5) Involvement R a t i o The involvement r a t i o s i s defined as the r a t i o of the a i r p o r t ' s passenger volume to the a i r c r a f t ' s a v a i l a b l e seats. I t i s a l s o not w e l l measured - e s p e c i a l l y f o r m u l t i - s t o p f l i g h t routes. (6) Maximum Passenger Loads This i s the l a r g e s t load of e i t h e r enplaning or deplaning passengers. I t i s n e i t h e r commonly used nor measured. The problem w i t h the use of m u l t i p l e c r i t e r i a was that one c r i t e r i o n might i n d i c a t e a d i f f e r e n t STEP s i z e than the others d i d . This o f t e n made s e l e c t i o n of a s i z e a matter of judgement. To s i m p l i f y the process of s e l e c t i o n , the l a t e s t d r a f t (1983) of the STEP Planning and Design M a n u a l 2 0 proposes that the e n t i r e s e l e c t i o n be based on a h a l f - h o u r l y design volume of passengers. Again, there i s no o f f i c i a l d e f i n i t i o n of t h i s volume, although the 90th p e r c e n t i l e by passenger volume i s o f t e n used. This approach places a great deal of emphasis on a s i n g l e design value. An e r r o r i n the measurement of the value or i n i t s f o r e c a s t i n g can l e a d t o an erroneous STEP s e l e c t i o n . For example, an e r r o r of the order of magnitude of ten passengers above the a c t u a l h a l f - h o u r l y volume would cause s e l e c t i o n of a STEP 6 t e r m i n a l , when a STEP 5 would have been s u f f i c i e n t . More research i n t o the behaviour of small t e r m i n a l f l i g h t loads should improve the accuracy of design volume c a l c u l a t i o n s and, t h e r e f o r e , the s e l e c t i o n of appropriate b u i l d i n g s i z e s . 2.2 Design Volume Determination There are a multitude of design volumes f o r passengers. S t a t i s t i c s 18 can describe annual, daily or hourly volumes. They can be classified by origin and destination or by enplanement and deplanement. These can be further broken down into major carrier, charter, domestic, transborder or international categories. Terminal design i s usually based on a peak hourly design volume. Half- hourly and six-hourly periods are also used. Definitions of what constitutes the peak hour abound. Horonjeff 1 1 suggests that a planner simply select a reasonable volume. The American Federal Aviation Authority 1 3 suggests the busiest hour of the busiest day of a typical week. Although American airports are not guided by a single body, many seem to favour the use of a percentage of either the annual t o t a l 8 or the average day of the busiest month19. Other definitions proposed include the peak hour of the average weekday in the busiest quarter and the nth highest hour of a l l hours of the year. Until recently Transport Canada 1 7 has used an hour or half-hour percentile definition. For larger airports, the accepted planning volume was the 90th percentile of the annual distribution of passengers. This more s t a t i s t i c a l approach relies on the prediction of the upper t a i l of a distribution curve. In the absence of complete data, some assumptions must be made as to the form of this curve. Some terminal design procedures rely heavily on the hourly (or half- hourly) design volume. For example Transport Canada's STEP method uses i t . Simulation models may or may not make use of i t . Most of them simulate activity over the course of eighteen or twenty-four hours, and so require daily input instead (such as a flig h t schedule or the passenger/non- passenger ratio for each hour of the day). 19 Some of the inherent features of basing t e r m i n a l design on the hourly design volume are l i s t e d below. This compilation i s based on the comments of Braaksma 3, de N e u f v i l l e 8 , H o r o n j e f f 1 2 , and Hamzawi 1 9. (1) no commonly agreed upon d e f i n i t i o n ; (2) very dependent upon a i r c r a f t s i z e , schedule and r o u t i n g ; (3) s t a t i s t i c does not incorporate s t o c h a s t i c v a r i a b i l i t y of the queueing process; (4) does not r e f l e c t i n d i v i d u a l a i r p o r t c h a r a c t e r i s t i c s such as type of t r a v e l l e r (commuter, v a c a t i o n e r ) or catchment area s i z e ; and (5) not d i r e c t l y u s e f u l f o r many computer s i m u l a t i o n s . 2.3 Passenger D i s t r i b u t i o n Functions Transport Canada has h i s t o r i c a l l y assumed that f l i g h t loads at sm a l l a i r p o r t s are normally d i s t r i b u t e d . This s e l e c t i o n has been made f o r convenience o n l y , s i n c e i t has a l s o determined that the Normal i s not the best model f o r a l l cases. Transport Canada i s of the opi n i o n that each a i r p o r t f o l l o w s a d i f f e r e n t d i s t r i b u t i o n . A i r l i n e s (and the manufacturers who s e l l a i r c r a f t to them) have a d i f f e r e n t approach to the study of passenger loads. They are more i n t e r e s t e d i n the number of occupied seats i n the a i r c r a f t than i n the passenger volumes at the a i r p o r t s . A i r l i n e s use a d i f f e r e n t combination of the volumes. For example, i n Canadian P a c i f i c ' s Vancouver-Terrace-Prince Rupert-Vancouver f l i g h t , the a i r l i n e might be i n t e r e s t e d i n knowing the p r o b a b i l i t y of f i l l i n g the seats on the second l e g - between Terrace and Prin c e Rupert. Since there i s v i r t u a l l y no Terrace to P r i n c e Rupert t r a f f i c , t h i s would be the t o t a l of 20 those going from Vancouver to Prince Rupert (Prince Rupert's deplaners) and those going from Terrace to Vancouver (Terrace's enplaners). Therefore, the number of seats occupied is the result of th summation of two independent randomly distributed variables. It Is desirable, therefore for an airline to use a distribution form which i s additive - that i s , the summation takes the same distribution form as the parts. Of course, this would be only one reason for an airline to select a particular distribution, since i t is only one use for the distribution. L a u c h l i 1 4 selected the Erlang function during research for Swiss Air to determine optimal seating configurations of aircraft. Vella, Martin and Whale 2 2 continued this work for Quantas Airlines but decided that the normal and binomial distributions produced better results. Wang24 used an empirical distribution function to determine booking levels for Cathay Pacific's long haul flights. The behaviour aboard the aircraft, which interests the airlines, i s obviously related to activity at the airports, which is of interest in this work. For example, the availability of seats limits the number of passengers that may board the aircraft. Also, a second flight may be warranted at a certain point, even though the increase in demand is occurring at another stop in the fl i g h t route. Because of this close interaction, the frequency distributions that the airlines and the aircraft manufacturers have selected for use are of interest for airport terminal sizing. 3. METHODOLOGY 3.1 Data Description The flight load volumes came from eight airports in British Columbia. They were originally released by the airline carriers to Transport Canada in order to assist in the planning of airport terminal buildings. Although the carriers are not obliged to release this Information, they did so to ensure reasonable sizing of the f a c i l i t i e s which they w i l l be leasing and to promote co-operation with the government. The data was not, however, meant to be used publicly so the airports have been designated by letters (A through H). A l l of the flights occurred between 1978 and 1982 at airports with three jet stops or less each day. A l l flights were served with Boeing 737 jets. The l i s t of airports in Table II illustrates the years and flights of the available data. As described earlier, the term "flight event" w i l l be used for the sum of the deplaned and enplaned passengers during a single v i s i t of an aircraft. A "f l i g h t " w i l l be the total of a l l flight events that occur over the course of one year at the same time of day. Therefore, each flight w i l l contain 366 fl i g h t events or less. Flight events cancelled due to poor weather (a very common occurrence) were excluded. Also not considered were flights which ran for only a portion of the year. This meant that a distribution of a l l airport activity could not be assembled for Airport H since i t had several flights which ran In the summer only. The characteristics of flig h t events at small airports have simplified the analysis. Volumes of deplaned and enplaned passengers are 22 TABLE II Quantity of Available Data Airport Number of Designation Years of Data Flights Total Number per Year of Flights A 1981 2 2 B 1978 to 1982 3 15 C 1980, 1981 2 4 D 1979, 1980 1 2 E 1979, 1980, 1982 1 3 F 1980, 1981 1 2 G 1981, 1982 3 6 H 1980 to 1982 1 3 37 Flights equivalent to half-hourly volumes because the flight turnarounds are less than thirty minutes and because the flights are separated from each other. Furthermore, there are no connecting or transiting passengers to account for. The prevalence of triangular routing has been mentioned. A l l of the airports in this study are part of such routes - most of which originate or terminate in Vancouver. The routes with both stops included in this study are: Vancouver - A - C - Vancouver; Vancouver - F - G - Vancouver (or reverse); and Vancouver - H - D - Vancouver. The raw data was assembled and entered into APL computer language, such that each flight was a vector. The flight vectors have from 137 to 361 elements. Each element is a flight event. To analyze distributions for airports with more than one f l i g h t , the flight vectors for that year were concatenated. The descriptive details of these variables are given in Tables III and IV. When arranged into frequency classes, the histograms had a right skew. A good model should reproduce this tendency. 3.2 Features of the Distributions Three model distributions w i l l be compared to the observed data. A more informed selection can be made i f the characteristics of each one are understood. The Normal or Gaussian is the most widely used of a l l frequency distributions. Its formula i s : 24 TABLE III Data Description for Flights Airport Flight Number of Flight Events Total Number of Passengers Year A Al 292 18,957 1981 A2 358 32,694 1981 B Bl 137 12,629 1978 B2 247 28,167 1979 B3 258 32,201 1980 B4 287 30,809 1981 B5 222 21,059 1982 B6 259 17,813 1978 B7 291 24,884 1979 B8 274 26,074 1980 B9 279 25,726 1981 BIO 167 16,154 1982 B l l 339 39,195 1978 B12 291 34,316 1979 B13 273 34,359 1980 Bl4 294 16,519 1981 B15 291 30,682 1982 C CI 332 15,388 1980 C'2 196 12,010 1980 C3 317 13,225 1981 C4 357 19,816 1981 D DI 328 1979 D2 352 23,857 1980 E El 361 36,607 1979 E2 360 42,031 1980 E3 354 29,899 1982 F Fl 344 36,941 1980 F2 358 40,427 1981 G Gl 344 13,995 1981 G2 352 28,758 1981 G3 313 44,647 1981 G4 328 13,964 1982 G5 343 27,324 1982 G6 329 43,684 1982 H HI 355 30,790 1980 H2 328 28,664 1981 H3 331 24,705 1982 25 TABLE IV Data Description for Airports Airport Year Combination Number of Total Number of Flights Flight Events of Passengers A 1981 Al + A2 650 51,651 B 1978 Bl + B6 + B l l 735 69,637 1979 B2 + B7 + B12 829 87,367 1980 B3 + B8 + B13 548 60,455 1981 B4 + B9 + B14 860 73,054 1982 B5 + B10 + B15 680 67,895 C 1980 CI + C2 528 27,398 1981 C3 + C4 674 33,041 D 1979 Dl 328 1980 D2 352 23,857 E 1979 El 361 36,607 1980 E2 360 42,031 1982 E3 354 29,899 F 1980 Fl 344 36,941 1981 F2 358 40,427 G 1981 Gl + G2 + G3 1009 87,400 1982 G4 + G5 + G6 1000 84,972 H 26 f ( x ) = _ J e x p [_ I ( 1 1 H ) 2 ] 0" / 2 TT X i U = mean - parameter approximated by E — where n = number of data points. ( X i - x ) 2 a = variance - parameter approximated by E — x = variable value. The normal is a continuous distribution function that is symmetrical about i t s mean. It is commonly used to describe variations i n physical measurements. The sum of two normally distributed variables is also normally distributed. This term for this feature i s additive regenerative. The formula for the Poisson distribution i s : P ( r , - ^ r = discrete variable value X i u = mean = variance - parameter approximated by E —— approximated. It is used for such things as determining the number of accidents in a given time interval. It has a right skew, but this decreases as the parameter (u) increases. The Poisson distribution is also additive regenerative. 27 The lognormal distribution has the logarithm of i t s variable values distributed normally. Natural logarithms are usually used but another base is possible. The function for a base ten lognormal distribution i s : X X f(x) = xa. .4343 , "727 log r 1 / l o g i o ( x / t l x ) exp [- j ( )ZJ log The lognormal is a highly flexible distribution which skews to the right. It i s not regenerative by addition, however, but by multiplication. That i s , the multiplication of lognorraally distributed variables i s also lognormal but the addition of them is not. 3.3 Procedure After the data was assembled, an APL computer program (owned by I.P. Sharp Associates) formed each vector into a frequency distribution. The parameters of each of the three model distributions were calculated from the data, and the program compared the expected, curves to those of the observed data. The three quantitative methods used to make the comparison were: i) the "goodness-of-fit", as measured by the Chi-Squared s t a t i s t i c s ; l i ) the a b i l i t y of the model to predict the t a i l of the distribution, as measured by the 90th percentile; i l l ) ranking of the models by visual Inspection. 28 The quantitative procedures used are outlined in this chapter. Discussion of the two qualitative selection c r i t e r i a - the a b i l i t y of the models to be easily understood and their applicability - has been deferred until the next chapter. Three sources of uncertainty inherent in any curve-fitting are: i) the natural variation of the data due to i t s randomness (due to unknown factors); i i ) the s t a t i s t i c a l failure to effectively estimate the parameters from the data; i l l ) the fact that a given model Is poor for describing the curve. Only the latter two sources can be minimized with a larger sample. The data had to be grouped into intervals and the expected and observed frequencies of each interval studied. A cumulative distribution form would have eliminated the need to use intervals, but the APL program used was not able to construct i t . One inherent feature of histograms i s that each individual interval has a certain probability of matching the frequency that the model has predicted for i t . Even i f the model i s a good one, a perfect f i t over a l l intervals, while being the most lik e l y event, is s t i l l not very l i k e l y . As the number of intervals increases, a perfect f i t becomes more rare. If fewer intervals are used, f i t t i n g the data to the model is more l i k e l y . However, i f several models are under consideration, more of them w i l l f i t . This makes a selection d i f f i c u l t . Therefore, some sort of trade-off is needed. 29 Secondly, histogram class divisions should theoretically be made so that the number of data points is the same in each. For example, the region of higher frequency w i l l have narrower intervals. Even though this is s t a t i s t i c a l l y preferable, variable Interval widths are not commonly used. In any case, the APL program used had limited f l e x i b i l i t y . It was a standard s t a t i s t i c a l program and could only accept equal band widths. A band width of ten was selected for a l l distributions. This meant that the number of divisions ranged from 10 to 27, according to the spread in data values. The APL program used for the Normal and Poisson distributions i s shown in Appendix A. It is an Interactive program which requests end points and the class width from the user. It then requires a selection as to whether the Normal or Poisson distribution is to be f i t to the data. Originally, the lognormal curve f i t t i n g was done by taking the logarithm of each data point and then running the standard program with the Normal option. This approach proved to be unsatisfactory since the scale was the data logarithm. The histogram intervals could not be compared to those of the Normal and Poisson. A new program was written for the lognormal in order to permit direct comparison. It Is similar to the standard program (although less refined) and is listed in Appendix A. The body was written by the author (LN program) but the histogram plotting function (HISTO and CLASSIFY) were written by I.P. Sharp Associates. The three quantitative c r i t e r i a used were: the s t a t i s t i c a l f i t of the model; the a b i l i t y of the model to predict a design volume; and the overall f i t of the model as judged by a visual inspection. 30 3.3.1- Goodness-of-Fit Criterion The Chl-Squared s t a t i s t i c i s produced by the program as a measure of the "goodness-of-fit" of the model. It is used to decide whether or not a distribution should be retained or rejected. The Chi-Squared s t a t i s t i c i s not meant to be used to choose among models. The definition i s : k (o, - e . ) 2 x2 = I \ 1 1=1 6 i where o^ = observed frequency e^ = expected frequency i = index of interval The calculation should only be performed when the expected frequency of each interval i s at least five, otherwise distortions can occur. For frequencies less than five, intervals should be combined. The programs did not do this, so the Chi-Squared value was hand-corrected by the author. Original and corrected values are in Appendix B. A few of the flights could not have their Chi-Squared values corrected because the program did not display enough significant figures. These five flights were omitted from further calculations. Use of the Chi-Squared values w i l l be discussed in the next chapter. It should be noted, however, that several pieces of information have been obtained from the data. As described in Section 3.2, the Normal and lognormal have two parameters (the mean and variance) and the Poisson has one (the mean). These have been estimated by the average or the standard 31 deviation of the data (or i t s logarithm). In addition, the total number of flight events has been used to determine the expected frequencies. The degrees of freedom of each distribution w i l l depend upon this information. 3.3.2 Design Volume Criterion As previously mentioned, there are many definitions of the planning design volume. Knowledge of this distribution w i l l allow for a more informed decision as to which definition should be used. This study w i l l look at the 90th percentile of the flight events as a representation of the upper t a i l of the d i s t r i b i t i o n . The actual 90th percentiles were calculated from the observed data. Short programs were written to derive the expected figures. The Normal and lognormal were written in APL but the Polsson was written in FORTRAN. They are listed in Appendix A. The other percentile definition used for large Canadian airports. It is the 90th percentile by passenger volume - that i s , 10 percent of the passengers w i l l experience congestion. This i s in contrast to the above percentile definition which would allow 10 percent of the flights to be above i t and thus experience congestion. The second definition could have been used to measure the upper t a i l predictability, but i t is d i f f i c u l t to calculate and is usually only slightly higher from the 90th percentile by passenger event. Figure 3 illustrates the 90th percentiles by passenger volume load were calculated for comparison purposes. One other definition of the planning design volume Is also included. This i s based on the average load factor and is calculated by adding fifteen percent to the mean load factor and multiplying this by the total number of arriving and departing seats available: 32 [ m e a n l o a d f a c t o r + 1 5 % ] x [ / / a r r i v a l a n d d e p a r t u r e s e a t s ] B e c a u s e t h e l o a d f a c t o r I s t h e p r o p o r t i o n o f a v a i l a b l e s e a t s t h a t a r e u s e d , f o r a B o e i n g 7 3 7 w i t h 1 1 7 s e a t s t h i s e x p r e s s i o n r e d u c e s t o : [ ( m e a n d e p l a n e d + e n p l a n e d p a s s e n g e r s ) + > 1 5 j x [ 2 x 1 1 7 s e a t s ] L 2 x 1 1 7 s e a t s J L J = ( m e a n d e p l a n e d + e n p l a n e d p a s s e n g e r s ) + 3 5 . 33 FIGURE 3 90th Percentile by Flight Event and by Passenger Volume "x A x l x2 Deplaned + Enplaned Passenger Loads 90th percentile by flight event 90th percentile* by passenger volume 00 00 10 percent of flights [ / f(x)dx = .10 x / f(x)dx] X l 00 00 10 percent of passengers [ / x f(x)dx = .10 x J xf(x)dx] x2 = 34 3.3.3 Visual Inspection Criterion This somewhat judgemental method of histogram selection was included to ensure that there was some measure of the reasonableness of each model. It also allowed for detection of any unexpected deviations in the data or any trends in the curve-fitting. Since a l l histograms have equal Interval width, a visual comparison was given a ranking from best to worst and the results totalled. The rating was made on the basis of how the model matched the overall shape of the curve without trying to duplicate the Chi-Squared or 90th percentile measurements. 35 4. ANALYSIS 4.1 Criteria for Acceptance or Rejection 4.1.1 Goodness-of-Fit The Chi-Squared value was used to accept or reject a model distribution for each set of observed data. The number of acceptances among a l l of the flights or a l l of the airports was then calculated as a percentage. The s t a t i s t i c was not used directly to decide which of the three model distributions best f i t one particular flight or airport, since such comparisons are not i t s purpose. Acceptance of a model i s the "null hypothesis". This hypothesis states that there is no difference between the expected and observed curves that cannot be attributed to randomness. It i s assumed that the null hypothesis is true until i t has been proven otherwise. The onus i s , therefore, to prove that a model should be rejected. To generate the proof, the c r i t i c a l value of Chi-Squared is found from the theoretical Chi-Squared distribution: 2 Xa, v where v = the degree of freedom (number of intervals less the number of parameters estimated from the data) a = the level of significance (area under the Chi-Squared curve, above c r i t i c a l value). If the Chi-Squared value calculated from the observed and expected frequencies i s less than the c r i t i c a l Chi-Squared, the f i t i s a good one 36 and the null hypothesis i s true. The specified level of significance (a) 2 is equal to the probability that the calculated Chi-Squared (x ) w i l l 2 exceed the c r i t i c a l value (xa y) even though the f i t is a good one. Therefore, there i s a probability, a, of rejecting a model that was, i n fact, a good f i t . In this study, the comparison was made at three different significance levels: .05, .01, and .001. As the level of significance decreases, there is more probability of the model being accepted. This i s due to the reduction of the probability of rejecting the model, even though i t f i t s the data. This i s called a Type I error. But by lowering this probability, the chances of accepting a model that is actually a poor one are increased - a Type II error. Therefore, a balance is needed since minimizing one type of error increases the probability of the other. Both types can be reduced, however, by increasing the sample size. In this analysis, the Chi-Squared is not the only criterion for selection. Therefore, the total number of acceptances can be compared at the three significance levels without forcing a conclusive decision on this criterion alone. The calculated and c r i t i c a l Chi-Squared values are shown In Table V for flights and Table VI for airports. Table VII and VIII show the percentage of acceptance for each model at each s i g n i f i cance level. The results of Table VII for the thirty—seven individual flights show that the lognormal model was a s t a t i s t i c a l l y good f i t to the data more often than the Normal or Poisson. When the flights were combined to get yearly distributions by airport, a l l three models f i t less often, although the lognormal was s t i l l slightly more successful. 37 TABLE V (a) Comparison of Calculated and C r i t i c a l Chi-Squared Values for Flights Airport Flight NORMAL x2(d • o.f) X2.05 x2.oi X2.005 A Al 19.6 ( 7) 14.1 18.5 20.3* A2 29.5 (10) 18.3 23.2 25.2 B Bl 48.6 (11) 19.7 24.7 26.8 B2 23.0 (11) 19.7 24.7* 26.8* B3 22.3 (12) 21.0 26.2* 28.3* B4 28.1 ( 9) 16.9 21.7 23.6 B5 12.9 ( 8) 15.5* 20.1* 22.0* B6 64.0 (11) 19.7 24.7 26.8 B7 68.9 (12) 21.0 26.2 28.3 B8 49.5 (13) 22.4 27.7 29.8 B9 56.4 (11) 19.7 24.7 26.8 BIO 15.6 (11) 19.7* 24.7* 26.8* B l l 38.7 (14) 23.7 29.1 31.3 B12 46.1 (13) 22.4 27.7 29.8 B13 45.6 (15) 25.0 30.6 32.8 B14 213.3 ( 9) 16.9 21.7 23.6 B15 32.8 (12) 21.0 26.2 28.3 C CI 21.8 ( 4) 9.5 13.3 14.9 C2 12.7 ( 5) 11.1 15.1* 16.8* C3 10.2 ( 3) 7.8 11.3* 12.8* C4 53.0 ( 5) 11.1 15.1 16.8 D Dl 5.1 ( 6) 12.6* 16.8* 18.5* D2 13.3 ( 7) 14.1* 18.5* 20.3* E El 21.8 ( 8) 15.5 20.1 22.0* E2 16.4 (13) 22.4* 27.7* 29.8* E3 t F Fl 4.7 (11) 19.7* 24.7* 26.8* F2 41.0 (12) 21.0 26.2 28.3 G Gl t G2 t G3 20.1 (14) 23.7* 26.1* 31.3* G4 12.7 ( 5) 11.1 15.1* 16.8* G5 9.9 ( 9) 21.0* 26.2* 28.3* G6 21.8 (14) 23.7* 29.1* 31.3* H HI 7.0 ( 9) 16.9* 21.7* 23.6* H2 9.1 ( 8) 15.5* 20.1* 22.0* H3 21.5 ( 8) 15.5 20.1 22.0* Number of Acceptances 11 16 19 *Acceptance at this Level of Significance ( x 2 < X2^, M) tSignificant figures of program do not allow Ch-Squared calculations. Source: Freund and Williams'*. 38 TABLE V (b) Comparison of Calculated and C r i t i c a l Chi-Squared Values for Flights Airport Flight POISSON x2(d. o.f) X2.05 x2.oi X .005 A Al 39.2 ( 9) 16.9 21.7 23.6 A2 29.3 (12) 21.0 26.2 28.3 B Bl 43.3 (12) 21.0 26.2 28.3 B2 22.2 (13) 22.4* 27.7* 29.8* B3 22.0 (13) 22.4* 27.7* 29.8* B4 40.8 (12) 21.0 26.2 28.3 B5 29.6 (11) 19.7 24.7 26.8 B6 57.1 (10) 18.3 23.2 25.2 B7 97.7 (11) 19.7 24.7 26.8 B8 72.0 (11) 19.7 24.7 26.8 B9 89.5 (12) 21.0 26.2 28.3 BIO 19.6 (11) 19.7* 24.7* 26.8* B l l 48.7 (14) 23.7 29.1 31.3 B12 43.5 (13) 22.4 27.7 29.8 B13 69.6 (14) 23.7 29.1 31.3 B14 t B15 30.4 (12) 21.0 26.2 28.3 C CI 76.9 ( 8) 15.5 20.1 22.0 C2 50.4 ( 8) 15.5 20.1 22.0 C3 88.8 ( 6) 12.6 16.8 18.6 C4 92.1 ( 7) 14.1 18.5 20.3 D DI 27.3 ( 9) 16.9 21.7 23.6 D2 34.1 ( 9) 16.9 21.7 23.6 E El 37.1 (11) 19.7 24.7 26.8 E2 14.7 (14) 23.7* 29.1* 31.3* E3 24.6 (11) 19.7 24.7* 26.8* F Fl 20.3 (13) 22.4* 27.7* 29.8* F2 27.2 (13) 22.4 27.7* 29.8* G Gl t G2 55.2 (11) 19.7 24.7 26.8 G3 18.1 (14) 23.7* 29.1* 31.3* G4 24.1 ( 7) 14.1 18.5 20.3 G5 29.0 (10) 21.0 26.2 28.3* G6 36.6 (15) 25.0 30.6 32.8 H HI 27.7 (12) 21.0 26.2 28.3 H2 39.2 (12) 21.0 26.2 28.3 H3 45.9 (10) 18.3 23.2 25.2 Number of Acceptances 6 8 9 *Acceptance of this Level of Significance (x < X a v) tSignificant figures of program do not allow Chi-squared calculation. Source: Freund and Williams 4 39 TABLE V (c) Comparison of Calculated and C r i t i c a l Chi-Squared Values for Flights Airport Flight LOGNORMAL x2(d. o.f) X2.05 x2.oi X2.005 A Al 14.5 ( 7) 14.1 18.5* 20.3* A2 19.7 ( 9) 16.9 21.7* 23.6* B Bl 22.3 ( 9) 16.9 21.7 23.6* B2 3.4 (11) 19.7* 24.7* 26.8* B3 7.7 (12) 21.0* 26.2* 28.3* B4 19.6 ( 9) 16.9 21.7* 23.6* B5 4.1 ( 8) 15.5* 20.1* 22.0* B6 16.5 (U) 19.7* 24.7* 26.8* B7 21.5 (12) 21.0 26.2* 28.3* B8 16.7 (12) 21.0* 26.2* 28.3* B9 18.0 (12) 21.0* 26.2* 28.3* BIO 9.2 ( 9) 16.9* 21.7* 23.6* B l l 52.9 (13) 22.4 27.7 29.8 B12 34.0 (12) 21.0 26.2 28.3 B13 43.1 (14) 23.7 29.1 31.3 B14 53.4 ( 9) 16.9 21.7 23.6 B15 23.9 ( 9) 16.9 21.7 23.6 C CI 6.9 ( 6) 12.6* 16.8* 18.5* C2 14.1 ( 5) 11.1 15.1* 16.8* C3 3.7 ( 3) 7.8* 11.3* 12.8* C4 9.1 ( 6) 12.6* 16.8* 18.5* D Dl 11.2 ( 8) 15.5* 20.1* 22.0* D2 36.8 ( 8) 15.5 20.1 22.0 E El 18.2 (13) 22.4* 27.7* 29.8* E2 14.9 (12) 21.0* 26.2* 28.3* E3 2.8 (10) 18.3* 23.2* 25.2* F Fl 34.6 (11) 19.7 24.7 26.8 F2 41.1 (12) 21.0 26.2 28.3 G Gl 14.4 ( 6) 12.6 16.8* 18.5* G2 31.4 ( 8) 15.5 20.1 22.0 G3 16.1 (13) 22.4* 27.7* 29.8* G4 16.4 ( 6) 12.6 16.8* 18.5* G5 64.3 (10) 21.0 26.2 28.3 G6 35.8 (14) 23.7 29.1 31.3 H HI 26.0 ( 9) 16.9 21.7 23.6 H2 24.2 ( 8) 15.5 20.1 22.0 H3 28.1 ( 8) 15.5 20.1 22.0 Number of Acceptances 15 22 23 Accepted at this Level of Significance (x2 < x 2 a v) Source: Freund and Williams'* TABLE VI (a) Comparison of Calculated and C r i t i c a l Chi-Squared Values for Airports No. of Flights NORMAL Airport Year X 2(d. o.f) X2.05 x 2 .oi X2.005 A 1981 2 75.8 (10) 18.3 23.2 25.2 B 1978 1979 1980 1981 1982 3 3 3 3 3 92.6 53.9 82.0 132.6 55.4 (17) (16) (17) (15) (13) 27.6 26.3 27.6 25.0 22.4 33.4 32.0 33.4 30.6 27.7 35.7 34.3 35.7 32.8 29.8 C 1980 1981 2 2 34.7 52.8 ( 6) ( 5) 12.6 11.1 16.8 15.1 . 18.5 16.8 D 1979 1980 1 5.1 13.3 ( 6) ( 7) 12.6* 14.1* 16.8* 18.5* 18.5* 20.3* E 1979 1980 1982 } 21.8 16.4 T ( 8) (13) 15.5 22.4* 20.1 27.7* 22.0* 29.8* F 1980 1981 } 4.7 41.0 (11) (12) 19.7* 21.0 24.7* 26.2 26.8* 28.3 G H 1981 1982 3 3 270.7 194.1 (19) (18) 30.1 28.9 36.2 34.8 38.6 37.2 Number of Acceptances 4 4 5 *Acceptance at this Level of Significance ( x < X a v ) tSignificant figures of program do not allow Chi-Squared calculations Source: Freund and Williams (Reference 3) 41 TABLE VI (b) Comparison of Calculated and C r i t i c a l Chi-Squared Values for Airports No. of Flights POISSON Airport Year x2(d. o.f) X2.05 x2.oi X2.005 A 1981 2 58.5 (13) 22.4 27.7 29.8 B 1978 1979 1980 1981 1982 3 3 3 3 3 240.4 120.3 210.2 528.5 46.6 (14) (15) (15) (14) (14) 23.7 25.0 25.0 23.7 23.7 29.1 30.6 30.6 29.1 29.1 31.3 32.8 32.8 31.3 31.3 C 1980 1981 2 2 78.2 131.3 ( 9) ( 8) 16.9 16.9 21.7 20.1 23.6 22.0 D 1979 1980 1 27.3 34.1 ( 9) ( 9) 16.9 16.9 21.7 21.7 23.6 23.6 E 1979 1980 1982 37.1 14.7 24.6 (11) (14) (11) 19.7 23.7* 19.7 24.7 29.1* 24.7* 26.8 31.3* 26.8* F 1980 1981 \ 20.3 27.2 (13) (13) 22.4* 22.4 27.7* 27.7* 29.8* 29.8* G H 1981 1982 3 3 2230.0 1490.0 (14) (14) 23.7 23.7 29.1 29.1 31.3 31.3 Number of Acceptances 2 4 4 *Acceptance at this Level of Significance (x < X a v) Source: Freund and Williams'* 42 TABLE VI (c) Comparison of Calculated and C r i t i c a l Chi-Squared Values for Airports LOGNORMAL Nr> r»f Year Flights X 2(d .o.f) X2.05 x 2 . o i X2.005 1981 2 28.5 (11) 19.7 24.7 26.8 1978 3 71.5 (16) 26.3 32.0 34.3 1979 3 59.1 (17) 27.6 33.4 35.7 1980 3 52.7 (17) 27.6 33.4 35.7 1981 3 109.4 (16) 26.3 32.0 34.3 1982 3 28.2 (13) 22.4 27.7 29.8* 1980 2 9.2 ( 7) 14.1* 18.5* 20.3* 1981 2 9.3 ( 6) 12.6* 16.8* 18.5* 1979 1 11.2 ( 8) 15.5* 20.1* 22.0* 1980 1 36.8 ( 8) 15.5 20.1 22.0 1979 1 18.2 (13) 22.4* 27.7* 29.8* 1980 1 14.9 (12) 21.0* 26.2* 28.3* 1982 1 2.8 (10) 18.3* 23.2* 25.2* 1980 1 34.6 (11) 19.7 24.7 26.8 1981 1 41.1 (12) 21.0 26.2 28.3 1981 3 99.0 (19) 30.1 36.2 38.6 1982 3 75.9 (20) 31.4 37.6 40.0 Acceptances 6 6 7 A B H •Acceptance at this Level of Significance ( x 2 < X 2 ,,) Source: Freund and Williams 4 43 TABLE VII Acceptance Rate By Flight Level of S i gni f1cance ( a) Normal Polsson Lognormal .05 33% 17% 41% .01 47% 23% 59% .005 56% 26% 62% 44 TABLE VIII Acceptance Rate By Airport ( A l l Airports) Level of Significance (a) Normal Polsson Lognormal .05 25% 12% 35% .01 25% 24% 35% .005 31% 24% 41% 45 TABLE IX Acceptance Rate By Airport (Airports with Multiple Flights Only) Level of Significance (a) Normal Poisson Lognormal .05 0% 0% 20% .01 0% 0% 20% .005 0% 0% 30% 46 These results are somewhat misleading, however, since they include airports with only one f l i g h t , which are also included as single flights in Table VII. The airports which had multiple flights had a much poorer acceptance rate. In fact, the Normal and Poisson did not provide a good f i t even once. These results are shown by Table IX. It i s significant that the theoretical distributions f i t more poorly as more flights were included. This was to be expected as the flights at one airport can be distinct in their characteristics (average loads, days of the week, et cetera). The f i n a l outcome may be that these theoretical models should be used only to describe individual flights. 4.1.2 Design Volumes Tables X and XI l i s t the 90th percentiles by fli g h t event for flights and airports respectively. The predicted values for Normal, Poisson and lognormal functions were calculated from the estimated parameters. Short APL programs were used for the Normal and lognormal. The Poisson distribution required a separate program because of the rounding errors involved. The APL functions could not handle such high means, so a FORTRAN program was written. A l l are listed in Appendix A. The 90th percentile by passenger volume and the "mean load factor plus 15 percent" volume are attached for interest. Both are alternative definitions of the peak design volume and have been calculated directly from the data. Inspection of Tables X and XI reveals that both the Normal and lognormal provide reasonable predictions of the 90th percentile values. The Poisson distribution i s consistently low in i t s estimate. The average 47 • TABLE X Comparison of Actual and Predicted 90th Percentiles by Flight 90th Percentile by Event 90th Per- Mean Predicted Predicted Predicted c e n t i l e Load A i r p o r t F l i g h t Actual by by by by Pax Factor Normal Poisson Lognormal Volume + 15% A Al 89 91 76 93 98 100 A2 132 127 104 130 138 126 B Bl 141 133 106 132 161 127 B2 157 155 128 156 170 149 B3 168 166 140 169 180 160 B4 141 141 121 144 147 142 B5 129 126 108 128 135 130 B6 119 107 80 110 130 104 B7 143 133 98 135 159 121 B8 151 144 108 148 165 130 B9 146 140 106 143 162 127 BIO 144 142 110 147 156 132 B l l 163 162 130 170 169 151 B12 169 162 132 166 177 153 B13 188 179 141 186 201 161 B14 106 101 66 94 150 91 B15 151 145 119 149 159 141 C CI 66 65 56 67 74 81 C2 83 83 72 85 90 96 C3 58 58 51 59 61 77 C4 78 76 66 77 86 91 D DI 91 89 73 92 101 97 D2 95 94 79 99 103 103 E E l 136 137 115 142 145 137 E2 163 159 131 164 170 152 E3 122 121 97 122 132 120 F F l 144 144 121 152 150 143 F2 154 155 127 164 168 148 G Gl 61 63 50 66 75 76 G2 109 111 94 115 115 117 G3 198 192 158 197 206 178 G4 65 64 52 69 72 78 G5 110 112 92 123 114 115 G6 190 183 148 191 199 168 H HI 116 118 99 122 125 122 H2 115 116 100 120 124 123 H3 102 102 86 105 112 110 48 TABLE XI Comparison of Actual and Predicted 90th Percentiles by Airports 90th Percentile by Event 90th Per- Mean Ai r - No. of Predicted Predicted Predicted centile Load port Year Flights Actual by by by by Pax Factor Normal Poisson Lognormal Volume + 15% A 1981 2 119 115 92 115 132 145 B 1978 3 155 145 108 157 165 130 1979 3 160 154 119 161 171 141 1980 3 174 165 124 174 190 145 1981 3 139 136 97 149 155 120 1982 3 141 139 113 144 153 135 C 1980 2 74 74 62 76 82 87 1981 2 70 70 58 71 79 84 D 1979 1 91 89 73 92 101 97 1 95 94 79 99 103 103 E 1979 1 136 137 115 142 145 137 1980 1 163 159 131 164 170 152 1982 1 122 121 97 122 132 120 F 1980 1 144 144 121 152 150 143 1981 1 154 155 127 164 168 148 G 1981 3 162 150 99 165 189 122 1982 3 156 145 97 161 179 120 H 49 TABLE XII Average D i f fe rences Between Ac tua l and Pred ic ted 90th Pe rcen t i l e s Normal Poisson Lognormal For F l i g h t s 3.3% 24.9% 4.1% = E|predicted-actual|x 100% 37 For A i r p o r t s 4.4% 31.9% 4.0% = E1 predicted-actual|x 100% 17 * 50 difference between actual and predicted values are shown i n Table XII for both flights and airports. The Poisson is clearly unacceptable. A good model should predict the design volume within ten passengers i f i t i s to be used in the Canadian STEP method. For individual flights the Normal failed to do this twice (Flights B6 and B7) while the lognormal exceeded ten three times (Flights B14, F2 and G5). The Poisson, however, could only predict the 90th percentile within ten three times (Flights C3, G4 and G6). Similarly, for the airport values the Normal missed four times and the lognormal twice, but the Poisson was never within ten passengers of the actual value. The other two planning values show that the 90th percentile by passenger volume is slightly higher, but very close to the 90th percentile by event. The second definition (mean plus 15 percent) i s much more variable. 4.1.3 Visual Inspection The subjective ranking of the overall curve-fit is shown in Tables XIII and XIV. The lognormal was the most effective, followed by the Normal. The inspection also pointed out some of the trends in the data and in the models. The high peak and the right skew common in most of the histograms were not well reproduced by the Poisson and Normal distributions. Also, many histograms had at least one other secondary peak to the right of the highest peak. This second mode may be due to the upper limit of the aircraft capacity, but proof of this conjecture would be beyond the scope of this study. TABLE XIII Visual Inspection of Histograms for Flights Airport Flight RANKING (1=BEST FIT, 3=W0RST FIT) Normal Poisson Lognormal A Al 3 2 1 A2 2 3 1 B Bl 3 2 1 B2 2 3 1 B3 2 3 1 B4 2 3 1 B5 2 3 1 B6 3 2 1 B7 2 3 1 B8 2 3 1 B9 3 2 1 BIO 3 2 1 B l l 2 1 3 B12 3 2 1 B13 2 3 1 B14 3 2 1 B15 2 3 1 C CI 1 3 2 C2 1 3 2 C3 2 3 1 C4 2 3 1 D Dl 1 3 2 D2 1 3 2 E El 1 2 3 E2 1 2 3 E3 3 2 1 F Fl 1 3 2 F2 1 2 3 G Gl 2 3 1 G2 2 3 1 G3 2 3 1 G4 1 3 2 G5 1 2 3 G6 2 1 3 H HI 1 3 2 H2 1 3 2 H3 1 3 2 TOTAL 69 95 58 52 TABLE XIV Visual Inspection of Histograms for Airports RANKING (1=BEST FIT, 3=W0RST FIT) Mr. r\f INO* or Airport Year Flights Normal Polsson Lognormal A 1981 2 2 3. 1 B 1978 3 2 3 1 1979 3 3 1 2 1980 3 2 3 1 1981 3 2 3 1 1982 3 2 3 1 C 1980 2 2 3 1 1981 2 2 3 1 D 1980 1 1 3 2 1981 1 1 3 2 E 1979 1 1 2 3 1980 1 1 2 3 1982 1 2 1 F 1980 1 1 3 2 1981 1 1 2 3 G 1981 3 3 2 1 1982 3 3 2 1 H (incomplet e) TOTAL 32 43 27 53 One other note should be made about the models. The Normal distribution is able to handle negative values, which cannot occur in the real data. This causes a distortion of the expected frequencies i n the f i r s t left-hand interval. Since the Poisson and lognormal can handle positive values only, they are more representative of the lower frequency classes. Visual inspection can only indicate preferences among the models and any gross tendencies of the data. It cannot be used as an independent criterion for acceptance or rejection. 4.1.4 Ease of Use The Normal distribution i s the most prevalent of the three distributions. It is a common assumption made by analysts that the data they are dealing with f i t s a Normal pattern. Because of the familiarity and general understanding, the Normal is easy to use. The Poisson and lognormal are less common but are s t i l l known and understood by most engineers. A l l three distributions have parameters which are simple to determine and are tabulated in most texts, although the Poisson is not usually calculated for parameters greater than twenty. If standard stat i s t i c s computer programs are to be used, the Normal distribution is easier to find curve-fitting routines for. In this study, the data had to be scaled down by a factor of ten to use the Poisson program and a separate program had to be written for the lognormal. If an extensive program library Is available, of course, this problem w i l l not arise. 54 4.1.5 Applicability In terms of applicability to small airport design, the prediction of the planning volume is the most important feature of any distribution. The normal and lognormal did this acceptably well for simple distributions. More complicated calculations may need to be done to determine the design volume under changing conditions. For example, as t r a f f i c increases, the upper t a i l of the distribution w i l l be limited by the aircraft capacity. A truncated curve w i l l then have to be used. If the flight route has several stops, the passenger volumes of a l l the aircrafts w i l l have to be added, and then this distribution truncated. A distribution that was additive regenerative would simplify this calculation. Also, i f the function were additive (the Normal and Poisson are), i t could be assumed that i f the total of the deplaned and enplaned passengers followed the distribution, that both each separately would be distributed according to the same function. Deplaned passenger distributions and enplaned passenger distributions could be determined. 4.2 Selection of a Model Of the three distributions considered, none describes the data i n a l l situations. The lognormal i s , however, the preferred model - followed by the Normal. As measured by the Chi-Squared s t a t i s t i c , the lognormal provided a good f i t more often. None of the models were good at describing airports with multiple fl i g h t s . The percentages of acceptance do not indicate whether a model should be taken for use in a l l cases. The lognormal was a good f i t for 41 percent of the flights and 33 percent of the airports (at a 55 .005 level of significance), but no deduction can be made as to whether or not these percentages are sufficient to unconditionally use the lognormal model. The decision remains judgemental. With reference to t a i l predictability, both the Normal and lognormal perform reasonably well. Use of the Poisson would lead to serious errors. Visual inspection suggests that the lognormal is the better model, followed again by the Normal. The fourth criterion - that the model be easy to use - would lead to the selection of the Normal. There are no serious complications, however, with the use of the other two. Finally, the criterion that the model be applicable would indicate that i t be additive regenerative. Only the Normal and Poisson are. The original hypothesis of this work was that a s t a t i s t i c a l model could be found that would approximate the data well enough for use in the sizing of small airports. If a model i s to be selected, i t would be the lognormal, although i f an additive quality was required, the normal would have to be used. The Poisson distribution can be discarded according to most of the c r i t e r i a . Although a selection was made, there is some doubt as to whether or not any of the three distributions is satisfactory. If only planning design volumes are to be determined from collected data, either the lognormal or the normal is adequate. However, any analysis that requires use of the entire distribution should consider other models - perhaps one of the six listed In the beginning of this study. This is especially true i f airports with multiple flights are under analysis. 56 5. CONCLUSIONS 5.1 Assessment The f i n a l decision to use a s t a t i s t i c a l model has to ultimately depend upon professional judgement. The study illustrates that using distributions for different purposes can result i n the selection of different models for each purpose. The lognormal provided the best model overall, although i t had drawbacks. Some flights were better described by other distributions. Also, the lognormal did not have the additive feature of the Normal and Poisson. Nonetheless, the study had revealed some of the strengths and weaknesses of the three. The scope of the study can be categorized in three areas: the number of models considered; the data i t s e l f ; and the computer programs used. Three distribution models were studied. The Chi-squared test measured overall "goodness-of-fit" and the 90th percentile test measured t a i l predictability. The inherent assumption i n the entire approach was that the st a t i s t i c a l models assumed that the data was random, when actually the number of passengers choosing a particular flight depends on the complex interaction of many variables. The models incorporate these unknown forces as randomness. The data i t s e l f has particular features which simplify the study. First a l l of the airports were in British Columbia. Air transportation in this province has certain unique and consistent features. For example, there are relatively few towns and these are typically separated by mountain highways or waterways. Therefore, air travel i s more common than in other provinces. Also, most air t r a f f i c funnels through Vancouver or Calgary/Edmonton. The majority of flight routes originate and terminate at these c i t i e s . For example, a Canadian Pacific flight follows a triangular Vancouver-Terrace-Prince Rupert-Vancouver route since neither Terrace nor Prince Rupert can generate sufficient demand to warrant a single stop. Since there i s virtually no demand between Prince Rupert and Terrace, i t can be safely assumed that a l l enplaners at Terrace are bound for Vancouver, and that a l l of the deplaners at Prince Rupert came from Vancouver. Another feature of these flights i s that they are a l l served by Boeing 737 aircraft which have a capacity of 117 seats. This situation has evolved because the carriers have found the Boeing 737 to be the most suitable aircraft for the region, although this may change in the future. Furthermore, at these airports, f l i g h t events are isolated throughout the day. This means that there is no overlapping in the use of the f a c i l i t i e s . Lastly, the scope of the research was defined by the computer programs used. A s t a t i s t i c a l packaged program was used to calculate the Chi-squared values and to plot the histograms for the Normal annd Poisson distributions. It was found to be too restrictive for the Lognormal, however, and a separate program had to be written. Budgetary considerations limited the extent of the analysis In this regard. The scope - as defined by the models, the nature of the data, and the computer programs - did not seriously hinder the process. There Is no evidence that the use of a cumulative distribution form or a different s t a t i s t i c a l measure (such as the Kolmogorov-Smirnov) would have significantly changed the results. 58 The results of the design volume analysis were consistent enough to allow the conclusion that the Normal and Lognormal are satisfactory models. The purpose of this study was to further the planning of small airport f a c i l i t i e s . Once the correct distribution is known, i t can be used directly in, say, a Monte Carlo simulation where passenger loads are randomly sampled from the distribution. The simulation would then produce expected occupancies for f a c i l i t y sizing. The distribution can also produce specific planning volumes (hourly or half-hourly). F a c i l i t i e s are then sized from a method of proportions or from a selection process such as Transport Canada's STEP. A frequency model would also be needed to determine more complicated effects on the airport passenger volumes. It can quantify the effects of route changes and aircraft capacity. 5.2 Further Research The possibilities for further work are numerous. L i t t l e research has been done in the f i e l d of smalll airports for several reasons: (1) Carriers are not required to submit data by flight or by day to the government; (2) detailed study was never considered necessary since aircraft were small, and f a c i l i t i e s could be incrementally adjusted; (3) air carriers are reluctant to release detailed information to competitors; and (4) small airports have not been deemed as important as larger ones when research was to be done. 59 Increased reliance on a single design volume, as well as less the reduced availability of construction capital, may change this situation. Further research might include: (1) Consideration of other s t a t i s t i c a l models (Gamma, Weibull, Rayleigh, Negative Binomial, Beta, et cetera); (2) calculation and comparison of the 90th percentile by passenger volume as a design volume; (3) categorization of airports by parameters or by distribution type; (4) calculations of the effects of multi-stop flight routes with respect to aircraft capacity; (5) calculation and comparison of other percentiles (75th, 80th, 85th); (6) using a cumulative distribution form and a Kolmogorov-Smirnov goodness-of-fit measure; (7) consideration of the effects of a trend to smaller aircraft, especially the Dash 7 in British Columbia; (8) derivation of demand distributions from the measured load distributions; (9) analysis of the costs of errors i n forecasting the design volumes on a l l f a c i l i t i e s ; and (10) a network analysis for British Columbia air t r a f f i c . 60 REFERENCES 1. Ashford, Norman and Wright, Paul H. Airport Engineering. John Wiley & Sons, U.S.A., 1979. 2. Benjamin, Jack, R. and Cornell, C. A l l i n . Probability, Statistics and Decision for C i v i l Engineers. McGraw-Hill Book Co., U.S.A. 1970. 3. Braaksma, John P. A Computerized Design Method for Preliminary Airport Space Planning. Technical Report, Department of C i v i l Engineering, University of Waterloo, Waterloo, Ontario. October 1973. 4. Braaksma, John P. Time Stamping: a new way to survey pedestrian t r a f f i c in airports. Tr a f f i c Engineering and Control, Volume 17, Number 5, May 1976, pp. 204-206. 5. Braaksma, John P, and Ramsay, W. Alex. Air Terminal Design: Decentralization and Shape. Transportation Engineering Journal, ASCE, Volume 105, TE6, November 1979, pp. 669-714. 6. Bury, Karl V. Statistical Models in Applied Science. John Wiley and Sons, Inc., U.S.A., 1975. 7. Chatfield, Christopher. Statistics for Technology. Chapman and Hall Limited, London, 1976. 8. de Neufville, Richard and G r i l l o t , Michel. Design of Pedestrian Space in Airport Terminals. Transportation Engineering Journal, ASCE, Volume 108, TEl, January 1982, pp. 87-101. 9. de Neufville, Richard and Rusconi-Clerici Ignazio. Designing Airport Terminals for Transfer Passengers. Transportation Engineering Journal, ASCE, Volume 104, TE6, November 1978, pp. 775-787. 10. Dunlay, William, J., Jr. Simulation Model Validation: airport applications. Transportation Engineering Journal, ASCE, Volume 107, TE4, July 1981, pp. 401-412. 61 11. Freund, John E. and Williams, Frank, J. Elementary Business Statistics: the modern approach. Prentice-Hall, Inc., New Jersey, U.S.A., 1972. 12. Horonjeff, Robert. Planning and Design of Airports, Second Edition. McGraw-Hill Book Company, U.S.A., 1975. 13. International Air Transport Association. Airport Terminals Reference Manual, Sixth Edition. 14. Lauchli, U. Matching Transportation Capacity to a Stochastic Transportation Demand. Proceedings of Sixteenth Annual AGIFORS Symposium, Florida, 1976. 15. Ramsey, G.R. Stuart and Hutchinson, B.G. An Airport Terminal Pasenger Flow Model. Paper Presented at 63rd Annual Meeting of the Transportation Research Board, Washington, D.C, January 1984. 16. Soumls, Francois, Ferland, Jacques-A. and Rousseau, Jean-Marc. MAPUM A Model for Assigning Passengers to a Flight Schedule. University de Montreal, Centre de recherche sur les transports - #142, August 1979. 17. Transport Canada, Air. Airport Traffic Allocation Model, Manual. Document AK 41-02-300, Airports Branch. 18. Transport Canada, Air. CATA's National Aviation Forecasting Models and Other Forecasting Methods. TP #2046. Policy, Planning and Programming, March 1979. 19. Transport Canada, Air. Study of the Air Terminal Building Planning Standard. TP 4771E. (Salah G. Hamzawi). Policy, Planning and Programming, July 1983. 20. Transport Canada, Air. Systemized Terminal Expansion Program (STEP), Draft. Document AK 62-08-000, Airports Branch, September 1983. 62 21. Transport Canada, Air. Vancouver Airport Simulation Model User's Manual. (E.J.M. Greco and G.R. Haverty), Airports Branch, September 1974. 22. Vella John, Jaul Martin and Whale Les. Determining the Best Aircraft Seat Configuration. Proceedings of Twenty-First Annual AGIFORS Symposium, California, 1981. 23. Walpole, Ronald E. and Myers, Raymond H. Probability and Statistics for Engineers and Scientists, 2nd Edition. MacMillan Publishing Co., Inc., New York, 1978. 24. Wang, Ken. Modelling the Interaction between Payload Restriction, Passenger Demand and Reservation Booking Levels. Proceedings of Twenty-Second Annual AGIFORS Symposium, Greece, 1982. APPENDIX A COMPUTER PROGRAMS 64 APL PACKAGE PROGRAM TO COMPARE DATA TO NORMAL AND POISSON DISTRIBUTIONS ( I . P . SHARP S ASSOCIATES LTD.) FREQ 41981 ENTER THE FOLLOWING DATA. LEFT HAND END OF THE FIRST FREQUENCY CLASS ;YOUR DATA MI 11=26 30 CLASS WIDTH AND THE NUMBER OF CLASSES;YCUR DATA MAX=16H • : 10 13 DO YOU WISH A FIT DONE ON YOUR DATA? Y OR N Y NORMAL OR POISSON ? N OR P N (1) DATA MEAN = 79.46307692 AND STANDARD DEV. - 27.90987073 DO YOU WISH A HISTOGRAM ? Y OR N Y DO YOU WISH TABULAR OUTPUT ? Y OR N Y -ENDPOINTS- L R MID OBS o / o EXP o / o 20 30 25 .0 6 0.9 24.666 3.8 30 40 35.0 18 2.8 26.48 5 4.1 40 50 45.0 63 9.7 43.617 6.7 50 60 55.0 76 11.7 62.998 9.7 60 70 65.0 101 15.5 80.890 12.4 70 80 75.0 106 16 .3 91.276 14 .0 80 90 85.0 84 12.9 90.802 14 .0 90 100 95.0 51 7 .8 79 .188 12.2 100 110 105.0 39 6.0 60.912 9.4 110 120 115.0 42 6.5 41.614 6.4 120 130 125 .0 20 3.1 24.895 3.8 130 140 135.0 23 3.5 12.9 38 2.0 140 150 145.0 15 2.3 5.893 0.9 150 160 155.0 4 0.6 2.408 0.4 160 17 0 165.0 2 0.3 1.420 0.2 TOTAL OBSERVATIONS CHI-SQUARE 650 78.0976 OBSERVED- o : EXPECTED- e : VARIABLE (COLUMN NO'. ) 1 150| 100 50 O O o e o o e o e « e » e • o e e o » e I 50 e o o o o o I 100 o o e e a e 150 200 65 APL PROGRAM TO COMPARE DATA TO LOGNORMAL DISTRIBUTION V LN w;LOGMEAN;LOGSD;LH;RH;RHO;ST ART;END;FRQ;PROB [ 1 ] LOGMEAN+-MEAN (1 0®GJ ) [2] LOGSD+STDDEV{l{»u) [3] MS+LOGMEAN,LOGSD [4] ' LEFT HAND END ' C5] LH+Q [ 6 ] ' RIGHT HAND END ' [7] RH+Q L8] VECTOR+LH ,LH+(10*i((.RH-LH)*10)) [ 9 ] LOGVECTOR+10W ECTOR c i o : ) PROBHL(0.5+(MS NORMALPROB LOGVECTOR)*10QQ))*\QM d i : ] RHO+pPROB L 12: 1 STARTSLH-10),VECTOR C13: 1 EN D+-V ECTOR, (RH+10) d u : 1 FRQ<-PROB*pu> [15: ] EXP+-LOGV ECTOR CLASSIFY (1 0®CJ ) [ie: ] DELH (FRQ-EXP) * 2 ) [17; ) Z>£X-KL(0.5+££7:xlOOO))*1000 [18. 1 ' ' [19: ] ' LH RH PROB EXP OBS X* [20 1 * ' [ 2 1 . ] SC+-v(.(RHO,l)pSTART) [22. } EC*-l((RHO,l)pEND) [23. ] PC*-f((RHO,l)pPROB) [2U ] FC<-v((RHO,l)pFRQ) [25 ] ECHAR+l((RHO,1)pEXP) [26 ] DCo-i({RH0.1)pDEL) [27 ) SC,' '.EC,' ',PC,' ',FC,' ',ECHAR,' ',DC [28 ] ' ' 0 ' ' [29 ] CS-r+IDEL [30 ] 'CHI-SQUARED = \ T ( C 5 ) [31 ] ' ' 0 'TOTAL OBSERVATIONS - ',T(paO [32 ] • • 0 • ' [33 ] EXP HISTO FRQ . , [3U 1 * 9 V . S u b r o u t i n e s HISTO and CLASSIFY on n e x t page. 66 SUBROUTINES 'HISTO' AND 'CLASSIFY' USED IN APL PROGRAM 'LN' VHISTOIOH V Ri-EXP HISTO 0BS\UI0\H\HH\TEST\B001\B002ILBL Cl] *FOR EXPECTED AND OBSERVED VALUES [2] DTCn-0 L3j H-[/EXP.OBS 0 £C2>10*Ll0®ff 0 HH-SCL* 1 1.5 2 3 4 5 6 8 10 [ 4 ] H+-L/(HHZH)/HH [5] TEST*-(\20)xH*20 0 B001+-TEST* .<EXP 0 B002*-TEST° .<0BS [6] R+e' o*9'LB001+2*B002] [ 7 ] 7 M ( 4 x i + ptf)p 0 0 0 1)V? nSPACE IT OUT A BIT [8] iW?,[0] [9] LBL+1 3 1 p#x l 0.5 0 0 LBL+(21plO*l)\LBL 0 R+LBL.R [10] LBL+-'EXPECTED: * OBSERVED: o' [11] ' ' O ' * 0 ' ' 0 ' ' [12] W--(pLBL)[UpR 0 R*-(W*LBL),lOl((l+pR),W)+R 7 VC£ASSIJFY[[]] V R*-a CLASSIFY CJ [1] if^i«.<u [2] /?-(l,[l] ff)-i?,[l] 0 [3] R++/R V [ 4 ] V 67 APL PROGRAM TO CALCULATE EXPECTED DECILES FOR NORMAL AND LOGNORMAL DISTRIBUTIONS vTfflVL[]]V V R+-TEN u\M\S\Z [:] M+-MEAN OJ [2] S+STDDEV u [3] Z--GAUSS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 U 3 V ( L i n e 4 w i t h o u t '10*' f o r Normal D i s t r i b u t i o n ) 68 FORTRAN.PROGRAM TO CALCULATE EXPECTED POISSON 90TH PERCENTILE L i s t i n g of P0I a t 13:34:50 on MAR 2. 1984 f o r CC1d=FCE6 1 C 2 C234567 3 REAL M,PROBRR,RR 4 DIMENSION R(20),P(20) 5 REAL Z.ZZ.F.D.DD 6 RR=100.0 7 M=64.9 8 C 9 R(1)=RR 10 C 1 1 DO 100 1=2.20.1 12 R(I )=R(1-1)+1.0 13 100 CONTINUE 14 C 15 F=0.0 1G PR0BRR=1.0 17 C 18 DO 200 d=1.200,1 19 IF (d.GE.RR) GO TO 210 20 F = F+ALOG10(FLOAT ( d)) 21 PROBRR=PROBRR+10**(FLOAT(d)*ALOG10(M)-F) 22 200 CONTINUE 22.2 210 CONTINUE 22.4 PR0BRR=PR0BRR*EXP(-1.0*M) 23 C 24 P(1)=PROBRR 25 DO 300 K=2,20 26 F=F+ALOG10((RR+FL0AT(K)-2.0)) 27 P(K)=P(K-1)+EXP(-1.*M)*10**(R(K-1)*AL0G10(M)-F) 28 300 CONTINUE 29 C 29 .05 WRITE(6,15)U 29. 1 15 F0RMAT('U WAS :',14) 29 . 14 C 29 . 15 WRITE(6, 18)PR0BRR 29 . 16 18 FORMAT('PROBRR WAS :',F9.7) 29 . 2 WRITE(6,13)M 29.4 13 FORMAT('PARAMETER :',F6.2) 30 WRITE (6,10) 31 10 FORMAT(' X +/PROB') 31.2 WRITE(6,12) 31.4 12 FORMAT (' ) 32 DO 400 1 = 1 ,20, 1 33 WRITE(6, 11)R(I ) ,P( I ) 34 1 1 FORMAT(1X,F4.0,3X,F5.3) 35 400 CONTINUE 36 C 37 STOP 38 END OUTPUT (Sample) 1 PROBRR WAS :0.5653268 2 PARAMETER :117.90 3 X 4 /PROB 4 5 120. 0. 565 6 121 . 0. 601 7 122. 0. 636 8 123. 0. 670 9 124. 0. 702 10 125. 0. 733 1 1 126. 0. 762 12 127. 0. 789 13 128. 0. 814 14 129. 0. 837 15 130. 0. 858 16 131 . 0 877 17 132. 0 895 18 133. 0 910 19 134. 0 924 20 135. 0 936 21 136. 0 946 22 137. 0 956 23 138. 0 963 24 139. 0 970 APPENDIX B DETAILED CHI-SQUARED CALCULATIONS 70 APPENDIX B TABLE BI X2 CALCULATON FOR THE NORMAL DISTRIBUTION BY FLIGHT PARAMETERS INITIAL CORRECTED Airport Flight NUMBER OF NUMBER OF u a DIVISIONS X2 DIVISIONS X2 A Al 64.9 20.4 13 78.8 10 19.6 A2 91.3 27.6 14 29.6 13 29.5 B Bl 92.2 32.0 20 80.0 14 48.6 B2 114.0 32.1 20 47.5 14 23.0 B3 124.8 32.3 20 26.9 15 22.3 B4 107.3 26.6 14 30.3 12 28.1 B5 94.9 24.5 16 25.5 11 12.9 B6 68.8 30.0 18 70.1 14 64.0 B7 85.5 36.7 18 83.5 15 68.9 B8 95.2 37.9 21 61.7 16 49.5 B9 92.2 37.0 18 59.7 14 56.4 BIO 96.7 35.0 20 24.7 14 15.6 B l l 115.6 36.1 19 41.8 17 38.7 B12 117.9 34.5 16 46.1 16 46.1 B13 125.9 41.5 19 46.8 18 45.6 B14 56.2 34.6 19 363.8 12 213.3 B15 105.4 31.1 19 38.7 15 32.8 C CI 46.3 14.9 10 46.7 7 21.8 C2 61.3 17.0 11 29.4 8 12.7 C3 41.7 12.4 8 17.7 6 10.2 C4 55.5 16.1 9 53.3 8 53.0 D Dl 62.3 21.1 11 29.7 9 5.1 D2 67.8 20.7 12 15.8 10 13.3 E El 101.4 27.7 20 51.4 11 21.8 E2 116.8 33.3 18 17.4 16 16.4 E3 84.8 28.7 20 305.7 * F Fl 107.4 28.8 20 42.5 14 4.9 F2 112.9 33.0 27 310.7 15 41.0 G Gl 40.7 17.6 12 658.8 * G2 81.7 22.5 18 378.8 * G3 142.6 38.3 17 20.1 17 20.1 G4 42.6 17.0 10 21.6 8 12.7 G5 79.9 25.1 20 121.6 12 9.9 G6 132.8 39.4 22 25.4 17 21.8 H HI 86.7 24.3 17 21.2 12 7.0 H2 87.4 22.7 14 10.7 11 9.1 H3 74.6 21.1 12 21.5 11 21.5 * Significant figures of the program do not allow calculatons of Chi-squared. 71 APPENDIX B TABLE BII X2 CALCULATON FOR THE POISSON DISTRIBUTION BY FLIGHT INITIAL CORRECTED Airport Flight PARAMETER NUMBER OF NUMBER OF y DIVISIONS X2 DIVISIONS X2 A Al 64.9 13 40.1 11 39.2 A2 91.3 14 29.3 14 29.3 B Bl 92.2 20 56.0 14 43.3 B2 114.0 20 25.1 15 22.2 B3 124.8 20 21.1 15 22.0 B4 107.3 14 40.8 14 40.8 B5 94.9 16 29.8 13 29.6 B6 68.8 18 62.8 12 57.1 B7 85.5 18 124.0 13 97.7 B8 95.2 21 93.0 13 72.0 B9 92.2 18 93.9 14 89.5 BIO 96.7 20 26.2 13 19.6 B l l 115.6 19 61.6 16 48.7 B12 117.9 16 43.5 15 43.5 B13 125.9 19 73.1 16 69.6 B14 56.2 19 1636.6 * B15 105.4 19 31.3 14 30.4 C CI 46.3 10 76.9 10 76.9 C2 61.3 11 50.5 10 50.4 C3 41.7 8 88.8 8 88.8 C4 55.5 9 92.0 9 92.1 D Dl 62.3 11 27.3 11 27.3 D2 67.8 12 35.5 11 34.1 E El 101.4 20 39.5 13 37.1 E2 116.8 18 15.6 16 14.7 E3 84.8 20 72.7 13 24.6 F Fl 107.4 20 29.7 15 20.3 F2 112.9 27 117.6 15 27.2 G Gl 40.7 12 61.9 13 * G2 81.7 18 60.6 16 55.2 G3 142.6 17 19.0 18.1 G4 42.6 10 24.4 9 24.1 G5 79.9 20 43.6 12 29.0 G6 132.8 22 56.8 17 36.6 H HI 86.7 17 28.3 14 27.7 H2 87.4 14 39.2 14 39.2 H3 74.6 12 45.9 12 45.9 Significant figures of the program do not allow calculatons of Chi-squared. 72 APPENDIX B TABLE B i l l X2 CALCULATON FOR THE LOGNORMAL DISTRIBUTION BY FLIGHT PARAMETERS INIT: [AL CORRECTED Airport Flight P a NUMBER OF NUMBER OF LOG LOG DIVISIONS X 2 DIVISIONS X 2 A Al 1.79 .14 13 15.6 10 14.5 A2 1.94 .14 14 20.7 12 19.7 B Bl 1.94 .14 18 31.8 12 22.3 B2 2.04 .12 20 10.1 14 3.4 B3 2.08 .11 20 9.4 15 7.7 B4 2.02 .11 14 20.4 12 19.6 B5 1.96 .11 16 9.1 11 4.1 B6 1.80 .19 17 18.3 14 16.5 B7 1.89 .19 18 23.6 15 21.5 B8 1.94 .18 21 24.1 15 16.7 B9 1.93 .18 18 23.4 15 18.0 BIO 1.96 .16 20 14.7 12 9.2 B l l 2.04 .15 18 56.0 16 52.9 B12 2.05 .13 16 34.3 15 34.0 B13 2.07 .15 19 45.9 17 43.1 B14 1.69 .22 19 77.7 12 53.4 B15 2.00 .13 18 26.4 12 23.8 C CI 1.64 .14 10 6.9 9 6.9 C2 1.77 .12 11 15.2 8 14.1 C3 1.60 .13 8 4.1 6 3.7 C4 1.73 .12 9 9.1 9 9.1 D DI 1.77 .15 11 11.2 11 11.2 D2 1.81 .15 12 43.9 11 36.8 E El 1.99 .13 20 67900. 16 18.2 E2 2.05 .13 18 19.0 15 14.9 E3 1.90 .14 20 11.3 13 2.8 F F l 2.01 .13 20 486. 14 34.6 F2 2.03 .14 27 21300. 15 41.1 G Gl 1.57 .20 14 26.5 9 14.4 G2 1.89 .13 18 1110. 11 31.4 G3 2.14 .12 17 16.1 16 16.1 G4 1.59 .20 10 32.7 9 16.4 G5 1.88 .15 20 34300. 13 64.3 G6 2.10 .14 22 809. 17 35.8 H HI 1.92 .13 17 32.6 12 26.0 H2 1.93 .12 14 24.6 11 24.2 H3 1.85 .13 12 28.1 11 28.1 73 APPENDIX B TABLE BIV X2 CALCULATON FOR THE NORMAL DISTRIBUTION BY AIRPORT (AIRPORTS WITH MULTIPLE FLIGHTS) PARAMETERS INITIAL CORRECTED Airport Year NUMBER OF NUMBER OF P a DIVISIONS X2 DIVISIONS X2 A 1981 79.5 27.9 15 78.1 13 75.8 B 1978 94.7 39.3 21 94.2 20 92.6 1979 105.4 37.6 22 55.1 19 53.9 1980 110.3 42.7 21 82.4 20 82.0 1981 84.9 39.5 20 133.9 18 132.6 1982 99.8 30.5 20 73.1 16 55.4 C 1980 51.9 17.2 12 60.1 9 34.7 1981 49.0 16.0 10 94.7 8 52.8 G 1981 86.6 49.4 23 276.2 22 270.7 1982 85.0 46.6 24 199.0 21 194.1 74 APPENDIX B TABLE BV X2 CALCULATON FOR THE POISSON DISTRIBUTION BY AIRPORT (AIRPORTS WITH MULTIPLE FLIGHTS) INITIAL CORRECTED Airport Year PARAMETER NUMBER OF NUMBER OF U DIVISIONS X2 DIVISIONS X2 A 1981 79.5 15 58.5 15 58.5 B 1978 94.7 21 255.4 16 240.4 1979 105.4 22 122.6 17 120.3 1980 110.3 21 226.1 17 210.2 1981 84.9 20 535.7 16 528.5 1982 99.8 20 49.3 16 46.6 C 1980 51.9 12 78.2 11 78.2 1981 49.0 10 131.3 10 131.3 G 1981 86.6 23 3411.9 16 2228.7 1982 85.0 24 2161.3 16 1488.9 75 APPENDIX B TABLE BVI X2 CALCULATON FOR THE LOGNORMAL DISTRIBUTION BY AIRPORT (AIRPORTS WITH MULTIPLE FLIGHTS) PARAMETERS INITIAL CORRECTED Airport Year NUMBER OF NUMBER OF LOG LOG DIVISIONS X2 DIVISIONS X2 A 1981 1.87 .15 15 31.2 14 28.5 B 1978 1.94 .20 21 1670. 19 71.5 1979 1.99 .17 22 62.1 20 59.1 1980 2.01 .18 21 58.0 20 52.7 1981 1.88 .23 20 109.4 19 109.4 1982 1.99 .14 20 43.2 16 28.2 C 1980 1.69 .15 12 9.4 10 9.2 1981 1.67 .14 10 9.6 9 9.3 G 1981 1.86 .28 23 103.1 22 99.0 1982 1.86 .27 24 91.0 23 75.9 APPENDIX C ACTUAL DECILES BY FLIGHT EVENT 77 APPENDIX C TABLE CI ACTUAL DECILES BY FLIGHT EVENT AIRPORT FLIGHT 10th 20th 30th 40th 50th 60th 70th 80th 90th A Al 42 47 53 58 63 69 74 80 89 A2 58 66 74 80 88 96 105 118 132 B Bl 59 67 75 80 84 88 97 113 141 B2 76 88 95 101 109 118 126 141 157 B3 86 99 106 115 123 128 136 149 168 B4 76 83 89 96 105 113 123 131 141 B5 67 74 81 86 92 98 106 114 129 B6 38 44 49 56 63 70 77 90 119 B7 46 54 61 67 77 87 101 115 143 B8 52 62 71 77 89 103 111 128 151 B9 49 59 66 75 86 98 110 124 146 BIO 56 68 74 84 93 101 111 127 144 B l l 69 81 92 102 115 127 138 150 163 B12 76 87 94 103 114 124 136 152 169 B13 75 94 103 109 120 131 147 164 188 B14 26 32 36 41 44 48 55 74 106 B15 70 77 84 93 100 111 122 135 151 C CI 29 35 38 41 44 48 52 58 66 C2 40 46 51 57 61 64 68 74 83 C3 28 31 34 37 41 44 47 51 58 C4 37 42 46 49 53 57 61 68 78 D Dl 38 44 50 54 60 65 71 81 91 D2 42 51 56 61 67 73 78 84 95 E El 69 77 87 92 98 106 115 122 136 E2 73 85 97 105 115 124 134 146 163 E3 51 61 67 74 81 89 94 105 122 F Fl 72 85 93 100 108 116 121 131 144 F2 78 89 97 102 109 116 125 136 154 G Gl 22 28 31 34 37 40 46 54 61 G2 56 65 72 76 81 86 91 99 109 G3 95 106 119 129 140 151 166 178 198 G4 22 27 33 37 41 45 50 57 65 G5 45 61 68 74 80 75 93 100 110 G6 79 99 111 121 130 141 156 165 190 H HI 54 65 73 80 86 93 100 108 116 H2 57 67 75 81 86 93 100 107 115 H3 48 59 64 68 73 79 84 91 102 78 APPENDIX C TABLE CII ACTUAL DECILES BY FLIGHT EVENT AIRPORT YEAR 10th 20th PERCENTILES BY 30th 40th 50th EVENT 60th 70th 80th 90th A 1981 47 55 62 69 75 81 90 104 119 B 1978 47 60 70 79 87 98 115 132 155 1979 60 71 84 92 101 111 122 139 160 1980 58 71 81 97 106 117 130 147 174 1981 36 46 56 70 82 93 106 121 139 1982 67 74 81 88 95 103 113 126 141 C 1980 32 37 41 45 50 54 60 66 74 1981 30 36 40 43 47 51 55 60 70 D 1979 38 44 50 54 60 65 71 81 91 1980 42 51 56 61 67 73 78 84 95 E 1979 69 77 87 92 98 106 115 122 136 1980 73 85 97 105 115 124 134 146 163 1981 51 61 67 74 81 89 94 105 122 F 1981 72 85 93 100 108 116 121 131 144 1982 78 89 97 102 109 116 125 136 154 G 1981 31 39 53 67 79 90 105 128 162 1982 31 42 55 66 77 90 104 122 156 APPENDIX D HISTOGRAMS 80 KEY TO HISTOGRAMS EXAMPLE FOR NORMAL AND POISSON U C cu u u CJ o o >1 o c 0) 3 <u M [=4 OBSERVED- o : EXPECTED- • : VARIABLE (COLUMN NO.) 1 1501 100 NUMBER OF ENPLANED + DEPLANED PASSENGERS EXAMPLE FOR LOGNORMAL NUMBER OF ENPLANED+DEPLANED PASSENGERS E x p e c t e d F r e q u e n c y D i s t r i b u t i o n O b s e r v e d F r e q u e n c y D i s t r i b u t i o n AIRPORT A, FLIGHT Al (Normal missing) POISSON OBSERVED- o s EXPECTED- • • VARIABLE f COL!. 7 5 SO.) I 50 2 5 o o o o o o o « « e o » ® » 9 9 9 » 9 8 9 • 90998999® ®09®»®9 0»8 00999S900G I I ! I 50 100 9 a o o s i i?0 LOGNORMAL EXPECTED: * OBSERVED: o 80 40 9 9 9 9 50 100 82 AIRPORT A, FLIGHT A2 OFSEEA'ED- 0 v TJ jr r< \ZTAPLE ':C0L;J':: • rO . } 1 7 5 | o 50 I o ® ® 1 o e * « « 1 o 9 ® 0 9 1 ® 8 e 0 9 8 1 9 e o o » 25 | C ® s ® o 0 s 8 1 9 ® s 8 o 0 9 0 o 1 9 8 ® ® e 0 o ® O s9 O 1 ® s ® 9 o 0 ® C ® ® 1 ® ® ® ® ® o 0 » o » ® s 0 1 o 1 1 1 1 1 » 1 1 0 50 100 150 200 OBSERVED- o : EXPECTED- ® VA RI A BIZ (coiv;:s so •) i 75 1 O 50 I O O 1 o O ® S 8 1 o « 8 O 8 1 o e 0 •a 1 8 8 8 0 O » 2 5 | o S 8 0 O 8 9 1 ® e » 8 o O 8 O s 1 o 8 8 » 8 o O 9 o s o 1 8 9 8 S 8 0 o 9 c S 9 » s 1 9 9® 8 8 8 o 9 o 8 9 O R 0 1 o 1 1 1 P o ! . ! 0 50 ICO : "0 • 2 f 0 LOGNORMAL EXPECTED: 60 OBSERVED: o 30 0 50 100 150 83 AIRPORT B, FLIGHT Bl NORMAL OBSERVE P- o "- » : Vf-r ftpi.p ( c o i v r v ro.) i u 0 | 0 | o 3 0 | o | o | 0 j o | o 2 0 | o o | o c o | o o » ® ® | 0 e ® ® 8 » | o 8 «  ®  ® 1 0 | o 8 ® ® ® ® o ® | ® ® ® ® ® ® ® o o ® | 9 ® 9 ® e © ® ® 0 0 ® | 8 8®® 8  ® o O O 0 ® o | O 0 ®  ® e a o C O O * ® ® 0 0 0 0 1 1 1 .1 I ] | s ® s | ® | 1 0 50 100 150 200 250 POISSON 0ESERV3V- o EXPECTED - 8 VA HIABLE ( COLU:'-' :;0 . ) 1 40 I O | O 3 0J . O | O | o | o | 0 2 0 ] o o | 0 o ® ® | o 8 ® O 9 | o S ® O 9 8 | o s 8 ® o 8 S 10 I o s 8 8 o 9 o 8 | ® ® 8 8 0 9 o O 9 | a ® o 9 c O 9 | © ® ® 8 ® o O 0 O « * 9 O | S O S ® S c O c C O S S O 9 O O C g [ 1 1 | | 1 | 9 S 8 | 9 | 1 0 50 1 CO 50 2 00 2 50 LOGNORMAL EXPECTED: 40 * OBSERVED: o AIRPORT B, FLIGHT B2 84 NORMAL POISSON OBSERVED- O EXPECTED- e : VARIABLE (coivn >Vf). ) 1 40 | ! o o 1 0 o 30 | 0 e e 1 o ® e 8 1 o e « 8 ® 1 o ® e ® ® « 1 o ® e ® e 20 | o ® e e ® 8 e 1 0 1 0 « ® e e 0 8 1 ® e ® « ® 8 o 8 8 1 o ® 8 e ® o ® * 1 0 | o 8 O ! 9 ® ® R S ® 8 o O e 1 ® ® e ® e ® 8 8 e c 0 8 ® 1 8 e 8 o « o 8 o O o 1 0 S c 8 o 8 * c 0 0 0 1 lo 1 1 1 1 I 1 * « ft 8 ' 1 0 5 0 1 0 1 1 2 0 0 OP-SERVED- o : F. XPF.CTETi-e VAPTARLE ' OOF,!!!' "0. ) 1 i+O | ! o O i 0 O 3 0 I o O 8 1 o » 8 ® 1 0 o » e 1 o e 8 « * 8 1 o « 8 s 8 8 2 o r O * ® * 8 8 8 i O 8 ® ® 8 « 8 ® i O « s 8 e 8 0 8 s i 8 ® « 8 8 O 8 8 i c » ® e 8 8 8 O 8 8 1 0 | o ® ® 8 8 ® c 8 C 8 1 ® s ® « 8 8 e 0 8 O C 8 1 ® e « 8 « e c ® o C 8 1 ® « ® ® « 8 ® 8 o 8 c O C 8 o 1 ® ® » ® ® * ® 8 o ® c O O ® e * o c 0 1 lo 1 1 1 1 1 * 8 8 1 0 1 CO 1 .=0 2 f 0 2 f 0 LOGNORMAL EXPECTED: * OBSERVED: o t o o o 9 ® ® S * e s 9 * 8 ® ® O • • • • • 8 ® 9 ® ® 8 ® 0 o ® « ® « « ® ® « * * ® ® ® ® ® 8 ® ® 9 ® ® ® ® ® 0 0 50 100 150 200 85 AIRPORT B, FLIGHT B3 NORMAL OBSEEVED- o FX? ECTED- 9 VA iii A BL; ( COLI •••.V ̂ 0. ) 1 ± 0 I 1 0 1 3 c j o O 1 o O 9 30 | o 8 8 9 ! o 8 20 I O O 9 | O o 8 9 9 8 o 9 -j 9 O 9 9 9 9 o 9 O | a o 9 9 9 8 o 9 8 | 9 o 9 9 9 * 0 O » 1C I 9 0 9 9 9 S o O 9 8 [ s 8 0 9 8 8 9 0 O 8 O 9 8 9 o » 9 9 8 0 O 8 O 9 | 9 O 9 S O 9 9 9 9 0 O 9 O 9 8 O | 9 . O O 9 9 o  » 8 9 o O 9 O 9 9 * o o o o 1 1 1 1 1 1 9 9 9 | 0 50 100 150 2 00 2 50 POISSON LOGNORMAL .OBSERVED- o EXPECTED- 8 : VA FT A ELI ( CO Lb - r. . ) 1 t o | | O | o O | o o | o O o 30 | o O 9 O | o 8 8 9 | o 9 9 8 8 | 9 9 9 9 8 | 9 9 9 9 9 2 0 | O ® a 9 9 9 O 9 | O c8 9 9 9 o 9 | o O 9 9 9 o 8 s | 9 O 9 8 8 8 o 8 8 | 9 O 8 99 9 o O 9 9 1 0 | 9 * O 9 8 8 o a 9 * | 9 9 O 8 8 9 o a 9 O 9 | 9 9 9 O * 9 » 8 o o » o O 9 | O 9 O 9 9 9 o 0 9 o c o s | » 9 O 8 8 O 9 » 9 * o o S c o o 9 9 9̂  0 1 1 1 1 1 I I ! ! ! ! 0 50 100 1 so "0 : 50 EXPECTED: * OBSERVED: o HO O O O O O a s 9 O 9 < > 9 O B 9 9 O * 9 6 9 9 20 9 9 9 S 9 9 9 9 9 9 9 9 9 9 * O 9 9 9 9 9 a 9 9 O 9 9 8 9 9 9 9 9 9 9 « B O 9 8 8 9 8 9 9 8 8 9 s B 9 O O 9 9 9 9 9 9 9 9 9 9 8 « 9 9 9 8 O 9 9 9 9 9 9 9 9 9 9 8 9 i 9 9 9 8 9 9 8 0-- 100 150 200 AIRPORT B, FLIGHT B4 86 NORMAL OBSERVED- o ED- 9 : VA P.I A ?i£ ( C01VK'<! 1 50 | 1 o 9 1 o ® ® 'S 1 o » ® 9 9 O 1 o 9 ® o c 9 O 2.5 | o ® s 0 O 9 9 | « » e o O 9 9 | 9 0 O S e & 1 ® e ® 9 0 O 9  9 9 1 ° e ® e  O O 9 » 9 0 9 o 0 1 1 1 1 1 « ® 1 50 100 150 2 0 0 POISSON - _ .. .. OBSERVED- o : E'/.PECl ED- 9 : VARIABLE ( COLVUS 1 50 | 1 o 1 o O 1 o ® 9 9 O O 1 0 o 9 O O 9 O 25 1 o 9 ® O O ® S 1 ® 9 ® O O 9 ® 9 l» s s ® 9 C C 9 9 O S » o 9 » ® O O 9 ® O 9 8 9 lo 0 9 9 ® o O ® ® O C O 9 O 0 1 1 1 ' 1 1 o | 50 100 150 2 00 - • LOGNORMAL EXPECTED: * OBSERVED: o 50 o * * 0 9 * 9 9* * O O 9 9 9 9 0 0 O 9 9 9 9 O » 9 ® a 9 9 O 25 9 9 9 9 9 9 O : : : : 9 9 0 • : i : : 9 9 9 : O 9 9 9 9 ® 9 9 9 9 9 9 9 9 9 9 9 9 9 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 50 100 150 AIRPORT B, FLIGHT B5 87 NORMAL " ' 0 - 9 VA ?.IA '. CCLW:: "'l>. ) i O O | o 0 9 | o 9 8 9 | o 8 8 ® 3 0 | o 9 8 O | o 8 9 o | 8 9 9 o 9 | s 9 8 0 8 | O 8 8 0 8 2 0 | O 8 8 o 9 | 8 8 8 8 o O 9 | 9 9 8 8 o O o | 9 8 9 9 O O o | 9 8 S 9 0 O O o 10 | 8 9 8 8 8 o O o 8' | o O o 9 | O 8 8 9 9 o O o 9 o | 8 0 9 8 9 8 o 0 0 9 9 | « 8 o 9 9 9 8 o o o 9 9 9 O O O 0 1 1 1 1 1 | 9 9 9 | 0 50 100 1 5 0 2 0-0 POISSON OBSERVED- o 1+0 30 EXPECTED- 8 VARIABLE { COlVy-S h'O. ) 1 20 10 9 1 O > O > O 5 0 9 9 © 9 I ICO 9 8 O o o I 1 50 9 O 9 2 0 o LOGNORMAL EXPECTED: i+0 OBSERVED: o 20 o 88 AIRPORT B, FLIGHT B6 NORMAL 0 3 a c a a 0 0 G 0 a a 0 a S £} a o o * (3 0 a a o a u a 0 a SI a SI o a o o a 0 a 0 8) a o O O 0 01 o o i i j j i a i s a a P O I S S O N V t D - o s EX;-' „-„C" ' t i : — a ; VAN I A 3 0 i ! " I a 0 SI a 1 o a c a i o a 0 o a 2 5 i o a a 0 0 0 i o a a c D 0 I a a a 0 q & o a i a a a a o c o o a o i o a a a 0 0 0 o G a i o lOo 89 AIRPORT B, FLIGHT B7 UfcSStKV NORMAL Jjl'lN o 0 u a a 3 0 0 a a a 0 a a a . 0 a 3) a a 0 Q 0 a a 0 a a a a 0 0 0 a a 8 a a a a a 8 0 D n 0 o > a a a a 6) a a 0 0 0 0 j a POISSON O B S E R V E D - o • E X P E I a W l f t i i L h i C O L U M N NO, ' / i. 5 0 I C) i 0 0 a 3 c a a a i o 0 £1 0 0 a a 25 i o o a 0 o a a £) i o a o 0 0 0 0 o a i a a £1 0 0 G c o a i c» a a a 0 0 O Q o o a G G i o a a a a  0 0 0 o o a a a o a o 0 i i j i i ; a a a a : 0 33 i :o ,. 0 2 CO LOGNORMAL - - EXPECTED: * 50 OBSERVED: o O o o o 25 9 * * 9 * o a ® * o a 9 a 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 ffi <ft * a 9 a 9 9 * * * a a a O O * a a a a a w TO *S 9 9 9 9 9 9 9 9 9 9 8 9 9 9 9 9 9 9 9 9 a 9 9 9 a a 9 a a 9 9 9 a 9 9 a 9 9 9 9 9 9 9 9 O 9 O O 9 9 O 9 9 a o 9 i O 9 O * * ® *® © © 9 9 9 9 9 9 9 9 9 ' > 9 9 50 100 150 90 AIRPORT B, FLIGHT B8 NORMAL O B S E R V c D - o • EX PL fc.L - V,- A B L E COL 0 ; Q 0 i 0 0 a Q a 2 5 i 0 0 3 a 0 0 0 i 0 a 0 a 0 G 0 a i 0 a a 8 0 0 G G a a i a 0 a a a a c 0 0 G a a a a c i a 0 a a a a D 0 0 0 o o a G y ) a [i 0 i o 1 1 1 o o I a a >;•! ; 0 5< ) IOC 15! ) 2 0 0 2 5 0 --• POISSON ObSfc.KVfc.JJ- o : E X P E C T E E - a v'AK I A B L E (COLUMN N O . ) 1 i 0 i 0 0 a e a 1 0 3 a a a 0 25 i 0 0 a a 0 0 a £) j 6 SI a s 0 G 0 a I o a a a G 0 G G a a ! o a a a 0 0 G G o a a o i a a a a a o 0 0 0 o a a a a o o 01 o ! t 1 1 © 8 « i O 8 C 0 50 11 i<3 150 2 0 0 2 3 0 a LOGNORMAL EXFECTED: * OBSERVED: o 50 o 0 0 O 9 9 9 * 9 9 * * 9 9 * * o 25 9 9 9 * 9 9 9 9 9 * 9 8 o 9 9 9 * 9 ® 8 9 8 9 9 9 9 8 9 O 9 9 9 9 9 8 9 9 * o 9 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 8 8 0 9 9 9 9 9 9 9 9 9 9 9 8 9 O O 3 9 9 9 9 9 9 9 9 9 9 9 8 9 9 9 * 9 9 9 9 9 9 9 9 9 8 9 8 9 9 9 9 9 9 9 9 ® 50 100 1 50 200 AIRPORT B, FLIGHT B 9 91 NORMAL POISSON OBSfc.KVb.D- o £XF'bC~ - a V A RIA BLE (CC fiN f iO. ) l 4 0 i i 0 i 0 s a 1 0 a a a 1 0 a a a a 3 0 1 0 a a e a 1 0 0 a a s a a 1 0 0 0 a • a a 0 1 0 0 SI a 0 a a 0 1 0 0 SI 8 0 a 0 0 a 2 0 i 0 0 a a 0 0 0 o . CI ! 0 0 CI a o 0 0 0 SI i o a a a 0 0 0 0 e> a i o a SI a 0 0 o 0 a CI i • a e> 8 0 0 0 0 0 o 1 0 1 o a a a • 0 0 0 a 0 0 1 a a S) a • 0 0 0 0 0 0 0 0 i a a a 6) s 0 0 o 0 0 0 a a 0 0 i a a a SI a 0 0 0 0 c 0 o a a 0 1 a a a 6) a 0 0 0 0 0 0 a a a a si u 0 0 1 i i 1 i 1 1 »:J i a l I 0 5 0 50 1 5 0 3 0 0 2 5 0 EXPECTED: * OBSERVED: o to 20 0 o * a * 9 a * 9 a * o 9 a a a * 0 9 9 9 a * o o 9 a a a * a o o 9 a a a 9 a o o 9 a a a a a 9 9 9 9 9 a 9 9 9 9 9 a a 9 a a 9 0 9 9 a a a 9 a 9 * 0 9 9 a a a 9 9 9 a a o * e 9 9 9 9 9 a 9 a a 9 o * 9 a a a 9 a 9 9 9 9 9 0 o o s 9 a 9 9 a 9 9 9 a 9 9 9 8 o e S 9 9 9 9 a 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 a a 9 9 9 9 9 50 100 150 200 AIRPORT B, FLIGHT BIO 92 NORMAL O B S E R V E D - o l>.D- a j V A R I A B L E (COLUMN NO i 0 2 0 1 0 0 0 1 0 0 a a a . 1 0 a a a a a a i 0 8 a a a 0 a 1 8) a a a a a 8) 101 8) 8) a a a C) a 8! a i 0 a 8) a a a a a 8) a a 1  a El a a a a 0 £) a a 1 a a a 0 6) a a a a 0 8) a o a 1 o a a S) 8) a a a 0  81 a a a 0 1 i 1 i • I 0 5< ) IOC 1 5 0 - 3 « | 3 2 0 0 POISSON JBStRVEu- o 3 0 I i I I I 2 0 I 10 i tXh'ECTtU- V A R I A B L t (COLUMN N O . ) i 0 a 0 a 0 a • 0 a 0 a a 0 a a 0 0 a 0 0 a a 0 0 a ei a a a 0 0 a 8) 0 8) a a 0 • 0 £•) a 0 a 8)' a a 0 0 a 8) a a 0 a 9! a a 0 0 0 a a a a a a a a o  c 6! a a a a a a • 0 0 a a a ICO I t O a i a 2 Co LOGNORMAL EXPECTED: * OBSERVED: o 30 15 O 9 * 9 9 9 9 O 9 9 9 9 O 9 9 9 a 9 0 * 9 9 a a 9 0 * 9 9 9 a 9 * 0 * 9 9 a a 9 * o 9 9 9 a a 9 * 9 O 9 9 9 a a 9 * 9 9 a 9 9 a 9 9 9 9 9 O 9 9 9 9 9 a a a 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 a 9 a a 8 9 9 9 9 9 a 9 9 a 9 9 a 50 100 9 O 9 9 * ® a a 0 150 200 93 AIRPORT B, FLIGHT B l l NORMAL O B S E R V t D - o : X P E C T E D - V A R I A B L E a 0 1 1 0 0 150 UMN pii'j . ) I. a 0 a a El 0 0 s a a SI a C! 0 a a 0 0 0 a a 0 0 a a a 0 0 0 a a a 0 a a a a 0 0 0 SI a a a a ci a a a 0 0 0 a a a a a ffl SI a a a 0 0 0 a a a «) a 2'JO POISSON O B S E R V L D - Q : E X P E C T E D- 0 : V A R I A B L E (C J L L MN NO . ) 1 5 0 i 1 0 a a SI 1 8 a a SI 8 I 0 a a a £> a s 0 25 i 0 a a 0 0 0 8 0 0 1 0 « a a 0 0 0 «l 0 8 0 i 0 a a s 0 0 D a o a a i 0 4) a e a 0 0 0 « o a a a I a si a a a 0 0 0 a D 8 a8 «) a 0 i s a a i I 1 i 1 i i o | i 0 50 1 0 0 150 no "250 LOGNORMAL EXPECTED: 50 * OBSERVED: o 25 o « 9 9 O 0 o o o 0 0 9 0 0 9 9 o 9 9 0 * 9 9 9 * 9 9 9 9 * 9 9 9 9 9 9 * 9 9 9 9 9 9 * 50 100 150 200 94 AIRPORT B, FLIGHT B12 NORMAL POISSON U d o b. P V b .U — G 1 E X P E L O E I — a V H R L - OLI. 'PIN N O . ) 1 4 0 i 0 1 i 0 0 a 0 i • 0 a a a SO 1 0 o 0 a a a i 0 Q 0 a a a 1 0 3 0 a a a r 1  a  a 8) a a 1 1 a a 0 a 8! a a 2 0 i • a a 0 0 8) a 0 G i 0 a a 0 0 6) D 0 8 0 i a a a 0 0 8) 0  0  1 a a a 0 0 8) 0 0 0 a 0 1 0 a a a • 0 8) 0 0 0 a 0 10 1 8) a a a 0 0 8) 0 • 0 a O C) 1 0 0     D 8)  D 0 a a D i a a a a a 3 0 0 8) G D 0 a a si a 1 a a si a a a • 0 a 0 0 0 a a 8) C! 1 o o a a a a 0 0 6) G 0 0 a a si o 01 1 1 i j i i 0 5 0 1.00 15< 2 0 0 ' O B S E R V E D - o E X P E C T E E - a : V A K I A t L E f: DLL UN N O . .1 j. 4 0 i i 0 1 o 0 1 0 0 a a 1 0 0 0 a 8) 3 0 i o • 0 a 8) a 1 0 0 0 a 8) a i 0 a 0 a 81 a a i 0 a 0 a 6) a a i 0 a 0 a 8) a a 2 0 1 0 9 a 0 0 8! e 0 a 0 : 0 a a 0 0 8) • 0 a 0 i • a a 0 0 8) 0 0 G 0 i a a a 0 0 a 0 0 0 0 0 i 0 a a a 0 0 a 0 D 0 a 0 10 i 0 a a a a 0 a 0 G G a a o a i a a a a 0 0 S) 0 0 0 a a o a i a a a a 0 0 a 0 O 0 a a a a. i a a a a a 0 0 a 0 0 G a a si o i a o si a a a 0 0 a 0 O G a a si i ; ' 0 1 0 i 5 0 i 0 10 i ! ;.:;'; 0 LOGNORMAL EXPECTED: * OBSERVED: O 40 o o 0 9 * 0 9 * 0 9 9 9 9 9 9 9 9 20 9 9 9 9 9 9 9 9 * 9 9 9 9 9 9 9 9 9 50 100 150 0 r r — AIRPORT B, FLIGHT B13 NORMAL V H n I A B L 4 0 : i o o o o a POISSON ObStRVtD- o tXKfcCI ED- a VARI L Jf-'IN NLi . ) 1 5 0 i 1 • \ • 0 401 0 i 0 i 0 1 0  0 3 0 1 0 a a a 1 0 8 a a 1 a a £1 « 8 I a 8 S) 0 a 0 a 0 S) 0 a 0 2 0 1 a a 0 0 0 a a i a a 0 a 0 a 0 8 1 a a 0 e> • • D a a a » • a 0 0 0 S) a 0 0 0 a a a 0 a 0 0 'o 0 0 0 0 10 1 0 «) a a a 0 a • c 0 0 a a 0 o a a a a 0 S! 0 0 0 0 o a o 0 c S) a 0 a 8 0 8) 0 0 0 0 o o a 0 C 0 it 0 Ci 3 a 0 c Q 0 0 o a a •3 G 8 8 £) O 0 o a 0 o 0 0 o o i) >:> 9 0 O " • 0 l 5 0 i t ) 0 1 50 i i i .'0 250 LOGNORMAL EXPECTED: * OBSERVED: o 50 O O O O O 9 O * 9 * O 25 * * 9 * 9 0 * 9 9 9 9 9 * 9 9 9 9 9 • * * 9 9 9 9 9 9 8 * 9 9 9 9 9 9 9 8 O 9 9 9 9 » 9 9 9 9 9 4 9 O O 0 * o 9 9 8 9 9 9 9 9 9 9 « 9 9 9 0 O * 8 9 9 9 9 9 9 9 9 9 9 « 9 9 8 9 O * 0 8 9 9 9 9 9 9 9 8 9 9 i 9 9 8 9 8 i 9 * 8 8 9 9 8 9 9 9 9 9 9 8 i 9 8 9 9 9 « 9 8 0- — ------ LOO 150 200 AIRPORT B, FLIGHT B14 96 NORMAL POISSON OBSEKVEJ J- 0 ' P F * ":TF Ei— a t V A R I A B L E CO' iiLUriN NO. ) 1 1 0 0 ! 0 /•-' ! 0 1 0 1 0 1 0 o 1 0 t) 5 0 i 0 0 1 a • 0 i a 0 0 i a 0 0 0 s ii a 1 a 0 a a ( 9 a a 2 5 1 a 0 a a a a a a 1 a a a a a a a a a 1 a a a a s J 0 a o a a 1 ' a a a a s ) 0 a • a a a 1 0 a a a a o 0 o o o • a a o o 0 0 1 i 1 i ! 1 o a ! a a a a a ] . 0 . 5 0 100 i SO 2 0 0 O B S E R V E D — 0 ; tXh'E i . : 1'fc.D- a : V A R I A B L E (OC iLOi lN MO . ) ;,. 1 0 0 I J 0 7 5 1 ' 0 1 0 1 0 i 0 o i • c: 5 0 i 0 o « 1 0 a a a i 0 a s a 1 0 c a o a a 1 0 a a a a a 2 5 1 0 a a o a a a 1 0 a o 0 6) a a 1 a a a a o a o a ; a a a o o a o a a a a a a o o 0 o o o a o o o a 0 1 i f ! ! a a a i a a a si a ; 0 b o - 10 0 15 0 2 0 0 LOGNORMAL EXPECTED: * OBSERVED: o 80 10 AIRPORT B, FLIGHT B15 97 NORMAL POISSON UBSEK'v'fc-iJ — G EX F E C 7 E D - a i 1" AC- 4 0 I o o 1 0 0 8  0 0 a a S) ! 0 0 a a 0 : 0 0 a 0 0 3 0 i 0 a a o 8 S) i  a a a  6) i 0 0 a 0 8 0 0 i a a a 0 8 0 8 I a a a 0 0 • 8 2 0 i a a a 0 0 0 8 1 a a a 0 0 0 a i a a a a 0 0 0 a 3 0 i a a a a 0 0 0 8 8 0 i a a a a 0 0 0 a a D 0 i o i a a a a a 0 0 0 a a 8 0 i 0 » a a a 0 0 0 a a a 0 i 8 8 0 a a a a 0 0 0 a a a a I a o o a e a a 0 0 0 « s 3 8 a I 0 0 0 a « « a 0 0 0 8 3 a a 0 £> 0 0 0 I 1 1 i i 1 1 8 | a 3 i i 0 5 0 L or 15C 2 0 0 2 5 0 O B S E R V E D - o : E X P E C T E D - a •• VA RI A B L E l O JU. MN NO•) i. 4 0 1 0 0 j 0 0 1 0 • 0 0 1 0 0 a 8 0 1 0 0 a 0 a 3 0 1 0 a a 0 a 0 1 0 a 8 0 a a l 0 a e 0 a 0 0 1 0 a a 0 a 0 0 1 0 a a 0 0 0 0 2 0 i a a a 0 0 0 3 I a a a  0 0 3 3 1 o . a a a 0 0 0 a o 0 i a a a a 0 0 0 8 0 0 1 o a a a 0 0 0 3 0 a C) 10 i a a 0 8 0 0 0 8 0 3 a i S) si a a a 0 0 0 8 0 a a 1 a s a a a 0 0 0 a o a 3 a i a o a a a a 0 0 0 a o 3 S) a 1 a a a e> a 0 a 0 o 0 a o 3 a o c a 0 100 I a 2 0 o AIRPORT C, FLIGHT CI NORMAL POISSON - - O D S E K v E D - E "EE - a ; VARIABLfc . (COLUi 'W NO. iooi i o 0 a i 0 a 7 5 1 0 a a l 0 a a 0 a CI 1 a a a 1 a a 0 5 0 1 a a 0 1 a a C) 1 a a 0 a 1 a a a 0 a 1 0 a a 0 0 v c i 1 0 a a 0 ' a 1 0 a a 0 CI i 0 0 a a a • 8 1 a 0 a a 0 0 a 0 1 a D a a 0 0 a a 0 1 0 1 1 I a 1 a i | 0 5C 100 1 5 0 O B S E R V E D - 0 S E X P E C T E E — a : V A R I A B L E < C 0 L 0I'l N N 0 . ; i. 1 0 0 i J 0 i 0 a 1 o 0 751 D 0 1 0 0 1 0 o o 1 0 a a 5 0 i a a a 1 a a a a i a a a 8) 1 a a a a a 1 0 a a a 0 a '-'5 1 0 a a a 0 a i 8 0 a a a 0 a 1 a 0 a a a 0 0 a 1 0 0 a a a 0 0 0 0 i a 0 a a a 0 0 o a a 0 1 0 1 i 1 o | 0 j i 0 50 1 CO 150 LOGNORMAL EXPECTED: * OBSERVED: o 100 ® 9 « a a a a a o a o 50 a * a a a a a a a 9 a a a a a o 9 9 9 9 9 9 9 9 a 9 9 ® 9 9 9 9 9 0 50 100 99 AIRPORT C, FLIGHT C2 NORMAL O B S E R V E D - a ; E X P E C " £> ; V A H I A B L E f CCL'JF'iN i'4 0 , } i i J 0 5 0 1 - 0 I a 8) i SI El i 0 0 S) SI 1 a c SI t) 2 5 i 8 0 £1 0 1 8 0 SI 0 3 J a 8 0 S) 0 8 i 8 a 0 6) 0 0 0 i e 0 a 0 SI a 0 3 0 1 0 1 1 j 3 8 6) 1 0 5 0 100 1 5 0 POISSON O B S E R V E D - o : E X P E C T E D - 7 5 i 5 0 i V A R I A B L E ( C O L U M N N O . > 0 I 8 3 0 0 0 o CI 0 0 0 0 8 SI 8 8 8 8) 8 8 8 SI 8 3 3 3 8) 8 3 3 8 8 8) 8 0 0 3 3 8 61 SI O 0 SI 8 SI I i- | 0 0 0 50 1 0 0 1 5 0 LOGNORMAL EXPECTED: * OBSERVEDt 0 60 Q O O O * O * 0 * © * . * ® ® ® ® ® ® ® O 30    0 ® $ ® ® ® ® ® ® e 9 e ® ® ® ® ® ® ® ® ® ® ® * 9 ® ® ® ® ® 9 ® ® ® © ® ® 9 * 9 ® ® ® ® ® ® ® ® ® 9 * ® ® ® 9 ® 50 100 100 AIRPORT C, FLIGHT. C3 O B S E R V E D - o E X P E C 1 c. L i - " a 2 V M P I r - i B L E ( C j L i. J n i'-i NO „ / i. i O O l a i 1 0 a a a | a a a a I a a I a a 1 a a a I a a a 5 0 i a a 0 0 a a 0 CI a a 6) a a 0 I 0 a 0 2 5 i a a ei 0 a a a 0 a 8 a a a 0 a a a a a Q a 0 a o a 0 a 3 0 1 i i 1 i i i a ! i 2 0 4 ;i SO I OO - • O B S E R V E D - o E X P E C T E D - a : V A K I A B L E ( C OLUi'lN NO . ) i 0 0 i 1 0 0 • 0 0 0 1 0 a 7 0 1 0 CI 1 0 a i 0 0 i a a i a a 5 0 1 a a a a a a a 1 a a a a 0 a a a 6; 8 a a a a £ 5 i 8 a a a a a 0 a a a a o a a 1 0 a a a a 0 a 0 8 SI a a a a a 0 a a a a 0 c a 0 i i 1 i ; o ; i 20 JO •;o SO .-. CO LOGNORMAL * a 0 a a 75 9 9 9 9 9 a s a 9 a 9 O * 9 9 9 9 9 9 9 a 9 9 9 9 a 9 a a 9 9 0 — 8 9 9 9 9 9 9 9 20 40 60 80 101 AIRPORT C, FLIGHT C4 NORMAL O B S E R V E D - 1 n o i 0 E X P E L : i L L i - a A B L E (C 3LUM* MO. ) es 0 I 0 a j 0 a 75 i Q a a 1 0 a a i a a a i a a c; i a a o . 5 0 1 a a 0 i o a a G a 1 5) a a Q a 1 8 a a 0 a i © a 8 0 a 2 5 i a a a o 0 1 a a a a 0 0 1 a a a a 0 0 a 0 1 s a a a 0 0 a 0 i 0 a a 3 0 0 8 a 0 0 i i 1 1 I ' ! i ; 8 i 1 2 0 .40 iO z'O 1 0 0 1 2 0 POISSON O B S E R V E D - 0 E X P E C l E D - 3 : V A R I A B L (COLUMN NO , ) 1 i oo i 1 0 - 1 • G i 0 0 1 0 0 7 5 1 0 o i 0 a I 0 G 1 0 3 0 5 0 1 3 e a I 0 a 8 8 8 I 8 a 8 8 a a a 8 8 " a 8 8 a SI a a 2 5 1 8 8 a 8 a 0 a I 8 8 SI a a o a a 3 1 a a a a a 0 0 0 3 l 3 a SI a a D 0 0 a . 1 0 8 a a SI G D c 0 o 1 2 0 i 4 0 i ! 6 0 i l 3 0 1 j 0 : 2 0 LOGNORMAL • EXPECTED: * OBSERVED: o 100 a 0 a a a a a a a a a a a a a a a a a a a 50 a a a a a a a a a a a a a a a a * a a a a a a a a 3 a a a a a a a 9 9 9 9 a a a a o a a 0 a a a a a a a a 40 60 80 1 0 0 102 AIRPORT D, FLIGHT Dl NORMAL - K V E D - I C) 8 SI 8 0 0 8 0 a SI a 0 a 8 8 0 a 0 8 a 0 0 a 0 8 8 0 0 8 a 8 8 0 0 a 3 0 8 a • 0 a s 8 e 8 a 0 0 8 s 0 8 0 a 0 0 a a 0 8 8 a 0 0 0 8 I I I I SI O E S E R V E D - E X P E c T E E - 8 : VAK i A E L i r . C C O U J h -i N O . ) i. 751 i CI 1 £1 1 1 0 o 5 0 1 0 8 a i 0 8 8 8 i 8 3 SI a 1 0 S3 a 0 0 a '| 0 8 a SI 0 8 2 5 1 a a a a 0 8 0 1 a a 8 8 0 3 0 1 a a a 8 SI 0 8 0 a P a a a SI • 3 c a si si o a a a SI 0 8 0 o a o 0 1 1 i j i i 0 5 0 1 i >o 1 5 0 EXPECTED: * OBSERVED: o 80 103 AIRPORT D, FLIGHT D 2 O B S E R V E D - NORMAL 0 : t ' X P E C r t L I - a V Af - 0 0 0 a a 0 0 a a 0 a a 0 a 0 a 0 a a a 0 a 0 a a 0 a 0 a a 0 a 0 3 a a 0 a 0 a a a a 0 a D D 0 a a a 0 a 0 0 a a a a a 0 a 0 D a 0 a a a a a 0 a 0 0 a a I 5 0 I A B L E (COLUMN NO. 1 0 0 1 5 0 POISSON O B S E R V E D - 0 ; E X F E TEE - a : V A R I A B L E (COL UflN NO . ) i 751 0 1 0 "l 0 C) 1 0 0 0 i 0 a 0 5 0 1 a a a 1 a a a a 1 a a a 0 1 a a a a o a 1 a a a a 0 3 2 5 i a a a a •0 a a 1 a a a a a 0 0 0 1 a a a a a 0 0 0 a a 1 a a a a a a 0 0' 0 0 a i a a a a a a a 0 0 0 0 0 0 i 0 1 ! i i i 0 0 1 '0 5 0 LOGNORMAL EXPECTED: 80 * OBSERVED: o 40 o o a * o a a o e a o a a o * a a a * a a a * a a a * e a a 0 a a a a a a a a a a a a a a a a a 9 a a a a a a a O 9 o a o 50 100 AIRPORT E, FLIGHT E l 104 NORMAL O B S E R V E D - o - 9 i A B L E < COLUMN N O . ) i 751 | 0 1 0 0 5 0 1 s a | 0 3 9 a 8 1 0 9 9 a a I a 0 9 a 8 8 j a 9 9 9 8 8 25 i a 3 a a 9 8 8 | a a a 8 8 8 8 8 | a a a 3 9 8 » 8 0 3 I a ai a 9 9 8 8 8 0 o a I a a a a a 3 8 8 8 si o o o a o o 01 a D 0 0 I 1 1 1 i a a a 1 a 1 . i 0 5 0 1 0 0 150 2 0 0 2 5 0 - • - ' - P O I S S O N O B S E R V E D - o : E X P E C T E D - 3 : V A R I A B L E (COLUMN N O . ) 1 7 5 l j a I • 0 0 5 0 i 0 0 1 0 a 8 « 0 I 0 9 8 9 a • | 0 8 8 8 8 8 | 3 8 8 8 8 a 2 5 1 8 e 8 9 8 3 3 i 8 8 3 8 8 a a a 8 I e a a a 9 8 a 8] 0 8 3 | a a 8 8 8 a a a 0 • 8. a 1 8 8 8 a 9 8 a 3 8) 0 o c o a 8) 0 1 8 a a o | 1 i i ; a i a i 0 50 100 150 200 - -0 LOGNORMAL EXPECTED: * OBSERVED: 0 60 O O O * o O * 9 0 * 9 0 9 9 9 9 0 9 9 9 9 O 9 9 9 9 9 0 9 9 9 9 9 O » 9 9 9 9 9 O 30 * 9 9 9 9 9 9 * 9 9 9 9 9 9 * 9 9 9 9 9 8 9 9 9 9 9 9 9 * 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 * 9 9 9 9 9 8 9 8 8 9 * 9 9 9 9 9 9 9 9 9 9 9 * * 9 9 9 9 9 9 9 8 9 9 9 9 i 9 O o ® 9 9 9 9 9 9 9 8 9 9 9 8 9 8 « 9 9 8 9 50 100 150 200 AIRPORT E, FLIGHT E2 105 NORMAL OBS ' t R v ' tD- 0 E X P E C 1 E D - a . V A H1 A E L L COLI ii-if •1 NO . ) i. 5 0 1 i a a 1 a G a i o a 9 G 8 a 1 0 0 a 0 a o a 2 5 1 • a 0 a 0 a 0 9 i e a o a 0 a o a a 1 6) 8 s 0 a 0 a o a a a 0 1 tl 0 8 a 8 o a 0 6) o a a a 0 1 0 0 8 e a D a 0 8 o a a a a £1 8 0 0 1 1 1 1 I i i a a | ! 0 5 0 i 0 0 15< i 2 0 0 2 5 O POISSON OBSERVEU- 5 0 i E X P E O T E B - V A R I A B L E (COLUMN N O . ) i 0 a a a • a a a a a 0 0 a a £) 0 a 0 a 0 a a a 0 a a 8 a 0 a a a 0 a 0 0 a a o a a a 0 8 0 a 0 a « a 0 a a a 0 a 0 a a 8 8 0 a a G a a a 0 a "0 a a 5 0 1 O 0 L 5 0 200 2 5 0 0 50 100 150 2 0 0 106 AIRPORT E, FLIGHT E3 NORMAL O B S E R V t D - h X P E C T L B - a i 0 5 0 t 0 0 3 i 0 8 8 e i 8 8 8 0 9 1 0 8 8 8 0 8 i 8 8! 8 8 0 0 9 -'5 i 0 8 8 8 8 0 0 3 ! 8 8 8 8) 8 3 0 0 0 8 1 8 8 8 8) 3 8 0 0 0 0 1 , e 3 3 6) 8 9 0 0 0 0 i 0 8 8 8) 8 8 0 0 0 0 1 0 0 150 ) 8 1 0 2 0 0 POISSON O B S E R V E D - o 7 5 < P E C T E D - 3 >I A B L E (COLUMN N O . : Q 0 0 8 0 9 8 9 8! 8 9 0 3 • 8) 8 8 0 9 O a 8 9 0 0 8 0 9 8) 8 a 0 0 8 0 3 8) a 3 0 0 0 a 8 8 8) 8 8 0 0 0 0 8 a 8 8 8) 8 9 0 0 0 0 0 0 8 8 8 8 3 0 0 0 o. 0 1 0 0 o a I • l 5 o AIRPORT F, FLIGHT F l 107 NORMAL O B S E R V E D - o : E X P E c T E D- a : V A R I A B L E ( C O L JMN MO . ) i. 5 0 1 0 1 a a a i a a a a i a a a a » 0 . _ . . .. . _ a " a a ' a a "a ~ 2 5 1 a a a a a a a • 1 0 a a a a a a a i S) 0 a a a a a a 0 i a a 0 a a a a a a 0 0 1 • a a a 0 a a a a a a o a a a 0 1 a a o I i : i 1 | i a a i a a I 1 5 0 1 0 0 i 5 0 2 0 0 2 5 0 POISSON O B S E R V E D - o E X P E C " " E D - a VAR I A B L E (COLUMI vi NO . ) 1 5 0 1 0 1 • 0 0 1 a a a C) I a a a a a 0 I a a a a a a -'5 i a a a a a a a a 1 o a a a a a a a i a o a a a a a a o a i a a o a a a a a a o o a 1 o a a a • a a a a a a o o o a a 0 1 a a o I 1 i 1 i 1 o" a 1 a a | 1 0 50 1 -0 15 0 2 Co 2'r0 LOGNORMAL EXPECTED: * OBSERVED: o 60 108. AIRPORT F, FLIGHT F 2 NORMAL O B S E R V E D - o ; E X P E C T E D - e • V A R I A B L E ( C C LUNN N O . ) 1 | 0 5 0 1 • 0 0 I 0 0 8 1 0 8 8 £•) 1 0 8 8 8 0 8 1 9 8 8 8 0 0 2 5 1 8 8 8 8 0 0 9 1 8 8 8 B 8 0 0 0 S i 8 0 8 8 8 8 0 0 0 0 8 i 8 9 0 8 8 8 8 0 0 0 0 0 f 9 3 0 0 0 0 8 8 9 0 0 0 0 0 0 8 0 0 0 1 8 8 0 | | ! 8 0 8 8 9 8 8 8 8 i 0 1 0 0 2 0 0 3 0 0 POISSON O B S E R V E D - o E X P E C T E D - V A R I A B L E < COLUMN N O . ) i a 0 0 0 0 0 8 0 8 8 8 0 8 8 8 0 8 8 8 9 8 0 0 8 9 8 9 9 0 0 9 8 8 8 8 8 0 0 0 8 0 0 8 8 8 8 0 0 0 0 8 8 0 9 8 8 8 0 0 0 0 0 8 8 8 0 0 8 9 8 9 O D 0 0 0 0 8 8 0 I I I 18888 8 880) ICO 2 0 0 SCO 109 AIRPORT G, FLIGHT Gl NORMAL O B S E R V E D - o 1 5 0 i I 1 0 0 0 0 0 0 S 8 0 8 0 8 8> 8 0 8 8) 8 0 0 8 8 0 0 8) • 8 8 0 0 0 8) 0 8 8 0 0 0 u i 0 0 ) 8 | 8 i oo 1 5 0 POISSON O B S E R V E D - 1501 i I I o : E X F ' E C T E D - 'VARIABL (COLUMN N O , ) 1 1 0 i 0 i 0 1 0 1 8 9 1 0 8 0 i 8 8 0 8 1 8 8 0 O j 8 8 0 0 I 8 8 8 0 0 1 8) 8 8 8 0 0 0 i o 0 I 0 8 | 8 100 1 5 0 LOGNORMAL EXPECTED: 150 * OBSERVED: o 110 AIRPORT G, FLIGHT G2 NORMAL POISSON S O B S E K V h L l - 0 E X P E C T E O - a V A R I A B L E (COLUMN N O . ) 1 7 5 1 0 1 0 0 0 a 0 a a 3 5 0 i a a a i a a a 0 1 a a a 0 1 a a a 0 3 I a si a s 0 0 2 5 i 0 si a a 0 0 1 0 si a a 0 o a 1 a 0 a a a D 0 0 1 0 0 0 si a a 0 0 0 1 a a • 0 si a a 0 0 0 si a 0 i 0 0 1 i 1 1 o a I a a a si j 0 5 J i oo 150 2 0 0 OBSERVED— 0 : E X h ' t C l"ED- a I V A R I A B L E (COLUMN N O . ) 1 751 0 i o 0 1 0 0 I 0 0 I 0 0 5 0 i a a 1 o a a a 1 a a s a 1 a a a a 3 I a si a a a CI ~'5 1 0 si a s> a • a 1 a 0 a a a a o a a 1 a 0 a si a a 0 0 si I s 0 0 si a a 3 0 0 D a i a a o 0 a a a 3 0 0 0 3 3 3 0 i a • i I i i 0 0 I 0 S! SI SI I o 5 0 100 150 2 O 0 LOGNORMAL AIRPORT G, FLIGHT G3 111 NORMAL O B S E R V b i J - o j t X P E C 1 E D- a X A b L E ( C JL MO, ) 1 4 0 i j L) 1 0 a a 3 0 1 0 a 0 a a 0 a 0 0 a a 1 0 0 a 0 0 a a 1 0 a a 0 0 0 a a 1 0 a a 0 • 0 0 a 2 0 1 a a a D 0 0 0 a C) 1 a a a 0 0 0 b a a 1 a a a a 0 0 0 0 a a 1 o a a a a 0 0 0 0 a a o a a a a • 0 0 0 a a a 0 10 1 a a a a a a 0 0 o o a a a o 0 ! a 0 a a a a a 0 • 0 0 a a a a 0 0 1 a e a a a a a 0 0 0 0 a a a a a a 1 o a a a a a a 0 0 0 0 a a a a a a • 1 o a a a a a a 0 0 0 0 a a a a a a 0 1 i 1 1 i 1 1 1 i 5 0 1 0 0 1 5C 500 2 5 0 POISSON O B S E R V t D - 0 : E X P E C " 'EE - a VA R I A B L f o : DLL MN N O . ) 1 401 J 0 a i 0 a a a 3 0 i 0 a 0 a a 0 a 0 0 a a 1 0 0 a D 0 a a 0 a a 0 0 0 a a 1 0 a a 0 D 0 0 a 2 0 1 a a a 0 0 0 0 a 0 1 a a a 0 0 0 0 a a 1 o a a a 0 0 0 0 a a I 0 a a a a 0 0 0 0 a 0 a 1 0 a a a a 0 o 0 0 a a 0 0 1 0 ! 0 a a a a 0 0 0 0 8) a D a 0 a 1 0 a a a a a 0 0 0 0 a a G a 0 0 1 0 a a a 8) a • 0 • 0 a a 0 a a C) 1 a a a a a a a 0 0 0 0 a a 0 a a 0 1 a a a a a a a G c 0 G 81 a 0 0 a 0 0 ! i 1 1 1 I ! j 50 100 1 50 jO 250 LOGNORMAL EXPECTED: * OBSERVED: o t o 112 AIRPORT G, FLIGHT G4 NORMAL POISSON O B S E R V E ! - 0 ; c X P E C T t E 3 : V A R I A B L E C O L U M N N O , ) i 7 5 i 3 / a a 8 a 8 a 3 D a 8 0 5 0 1 0 3 3 0 a 3 a 0 8 a 3 0 a a a 0 3 8 8 a 0 a 2 5 ! 8 a a 0 0 a a 9 8 0 0 a a 3 3 0 0 a a a 8 8 8 0 0 a 0 a 8 a 3 0 0 a 8 0 ij 1 1 1 1 3 1 f 5 1.00 O B S E R V E D - • ; E X P E C T E D - 3 ; V A R I A B L E ( C O L U M N N O . ) 1 7 5 I .0 1 0 0 1 0 8 ! 0 8 a 8 8 a 5 0 1 0 a 8 a 1 0  8 8 I a 8 3 a 8 1  8 8  a i 3 a a a a -;CT j 8 a 8 3 0 a 1 a 8 a 8 8 0 8 1 0 a a a 8 0 a 1 a 3 a a 3 0 0 3 a ! 8 a 3 a 3 3 0 0 D 0 0 i i 1 •1 0 5 0 1 0 0 LOGNORMAL EXPECTED: * OBSERVED: O 80 * a o * a o * a o * a a a a a a a a O a a a O a a a o a a a 0 HO a a a a a a a a a a a a a a a a o * a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a * a a a a 50 113 AIRPORT G, FLIGHT G5 NORMAL OBSERVED- o : -EXPECTED- 0 : VARIABLE (COLUMN NO.) 1 75| 50| 25| 0|* 0 o e e 0 0 0 0 » e « e 0 a 0 e e 0 o 9 O 9 0 9 0 0 0 9 0 0 0 0 0 9 0 0 0 0 9 0 0 0 0 0 0 O 1 I I I O 9|9 50 100 150 200 POISSON OBSERVED- O : EXPECTED- 0 : VARIABLE (.COLUMN NO.) 1 751 50| 25| 0 9 0 o o o O 0 9 O 0 0 O 9 9 9 0 O 9 O a o 50 I I o o| 9 0 9 0| • 10 o 15 0 200 EXPECTED: * OBSERVED: o 50 O o O O o 9 O o 9 0 0 * < 9 9 o O * i 9 9 9 O * i » 9 9 O O * B 0 0 o 0 t * » 9 9 o 30 t * » 9 9 o t * 9 9 9 o o t 9 9 9 9 9 O 9 ' 9 9 9 0 9 9 9 9 9 9 O 9 9 9 9 9 9 9 9 * * O 9 9 9 9 9 9 9 9 9 * * 9 0 9 9 9 9 9 9 9 0 9 9 9 9 9 9 9 9 9 9 100 150 114 AIRPORT G, FLIGHT G6 NORMAL O B S t K V h D - 4 0 i -• o : hXi '- 'hCTLD- a : • VAR I Al- L E (C OLUMN N O , ) 1 1 ii 0 00 1 u a e o 3 0 i o a ei a o o i ; o 8) a a o a a 1 a a a o o a o 1 - 8)8)8)0 083 i a a a o o o a 2 0 i a a a ei o o o s f aaaaoooaa i o a a a a a o o o a a o • 1 o o a a a a o o o a a s o I o a o a a a a o o o a a a o 1 0 i o a o a a a a o o o a 3 a a 1 aaoaaaaoooaaoat) i ©808888)000380880 i 88808aaaoooea0888 0 1 aaaasaoaaasioooaaoaaasia 0 1 oo I I i | i 0 1 0 0 2 0 0 3 0 0 POISSON O B S E R V E D - o : E x P E u 1 E D - a : VAK I Ab 'Lh < COLUMN NO ., ) 1 4 0 1 oaaa 8 8 8 8 3 0 1 o 8 a a o 8 o i o a a a o a o 1 a a a o o a a i a a a o o e a i | a a a o o o a 2 0 i aaaaoooea i 888 8 00080 1 o a a a a o o o a o o 1 088 a S 8) 000003 0 i 0088888) 000808 0 1 0 1 o o a a a a a o o o a o a a 1 o a a a a S) si o o o a o o a o 1 o a a a a a a o o o a o o o si o I o a a a a a a a o o o a o o a a a o a i o a a a a a a a a o o o a o o a a a a o 0 i 883 i i i | ICQ 2 CO \ 0 LOGNORMAL .EXPECTED: t o * OBSERVED: o 0 O * 9 9 * 9 0 O * 9 0 9 * o O * 9 9 0 9 o O * 0 0 0 9 9 O * * 9 0 0 9 9 o O * 9 0 0 9 9 9 9 O * 9 9 9 9 9 9 9 O O * 9 9 9 9 9 9 9 9 O O 9 * 9 9 9 9 0 9 0 9 9 O 0 9 9 9 9 9 9 0 9 9 9 9 O o 9 9 9 9 9 9 9 9 9 9 9 * o * o 9 9 9 9 9 9 9 9 9 9 9 * 9 O 9 9 9 9 9 9 9 0 9 0 9 9 9 9 9 0 * O 9 9 9 9 a 0 9 9 9 9 9 9 9 0 9 0 * 9 9 9 9 9 9 9 0 9 9 9 » 9 9 9 9 0 9 * 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 100 150 200 115 AIRPORT H, FLIGHT HI NORMAL OBSERVED- o : t X h ' h C TEL" - a V AR I ABLE (C 0 L U M N N 0 . 1 75 i 1 i 1 a a a 50 l a a s 0 1 0 a a 0 a 1 a a a 0 a i a a a 0 a 0 1 a a a • a a 25 1 0 » a a 0 a a 1 a a a a 0 a a 1 a a a a a 0 a a- a 1 a a a a a 0 a a a a i 3 a a a a a a 0 a a a a a 01 o 1 1 1 i o I a a a a j 0 50 1OC. 150 200 POISSON O B S E R V E D - o : E X P E C " "EE - a : V A R I A B L E (COLUMN N O . ) 1 751 1 1 • . 1 0 1 0 501 0 a 0 1 0 a a a a I  a a a a 1 a a a a a 0 i a a a a a a 251 a a a a e a a 8) i <i 8) a a a a a 81 1 a a 8) a a a a a 0 a 1 a e 8> a a a a a 0 o a 1 a a a a 8) 8) a a a a 0 o a a a 0 1 o 1 I i i o 1 o o a a I 0 - 5 0 100 1 5 0 2 0 0 LOGNORMAL EXPECTED: * OBSERVED: o 60 * O * a * * a * a a O a a O o 9 9 a O • a a a o a a a a O * a a a a a O * » 9 9 9 a O 30 * a a 9 9 9 O a a e 9 9 9 O a a a a a 9 9 9 a o a a a 9 9 a a a a a a a a a a a 9 9 9 9 9 a a a a a 9 0 a a a a a a a a 9 9 9 9 9 9 9 a a a a 9 * * a a a a a a 9 9 9 a a © ® ® © © ® 50 100 150 116 AIRPORT H, FLIGHT H2 NORMAL POISSON - O B S E R V E D - (J ; t: X r' b. L IE a VAR I A B L E (C OLUi lN N O . ) 1 75 i | a a 0 5 0 1 a a 0 0 1 a a 0 0 1 a a • 8 1 a a a 0 a 1 a a a 0 a a 2 5 1 0 a a a 0 a a i a a a ® - 0 a o 1 a a a" a 0 a o a 1 - a a a a a 0 a c a 1 a a a a a a 0 a o a a o 0 ! • 0 1 i i a a a ] ! 0 5 0 i OC 15C 2 0 0 O B S E R V E D - o E X F E C T E D - a V A R I A B L E X U M N NO'. ) 1 751 j 0 0 5 0 1 0 0 0 0 i 0 a a C! s a a a 8 i a a a a a 1 a a a a a a 2 5 1 0 a a a a a a i a a a a a a o a 1 a a a a a a a o o a - 1 0 o a a a a a a o o a a 1 a o a a a a a a o 0 0 0 a a 01 i 0 i ] i 1 0 0 i | 0 S o 0 It 0 20Q LOGNORMAL 60 30 * OBSERVED: o * 0 * 9 0 * 0 O 9 9 0 0 * 9 9 9 O * 0 0 0 0 * » 0 9 O * 0 0 9 O s 9 0 9 a 9 9 0 0 9 9 0 9 9 9 9 9 9 9 0 9 9 9 9 9 9 9 9 9 9 0 9 9 9 9 9 9 9 9 a o 9 9 9 9 0 0 0 o 9 9 9 9 9 9 9 o ^ 50 1 0 0 9 9 9 1 5 0 117 AIRPORT H, FLIGHT H3 NORMAL O B S E K V E D - 0 ; EXF _U- •E J — 8 ifilABLL- (COLUMN NI- ! . ) i i o i i 0 SI 0 i Si SI 3 5 0 1 S) 8 a ] SI 8 a i 8 SI 81 9 9 1 0 SI 8 8 0 1 0 S) 8 a 0 251 a 0 8) 9 8 0 8 i 0 0 SI 9 8 0 8 i 0 0 0 SI a 8 0 0 1 a o 0 8) 8 8 0 0 SI 0 i 8 9 0 0 81 a 8 D 0 8 SI 0 01 • i i 1 i a j 0 5 0 1 0 0 1 5 0 POISSON O B S E R V E D - o : E X P E C T E D - a V A R I A B L E (COLUMN NO - ) 1 / _i 1 1 ' 0 . I 0 i 0 0 0 1 0 0 0 5 0 i 0 9 0 1 SI a a i . S) 9 a 8 i 8 81 a a 0 i a si a 8 0 8 2 5 I 8 9 8) a 8 o 9 1 0 8 6) a 9 0 8 8 1 8 0 t SI 8) a 9 0 0 a 8 i 8 0 6 8) a 8 0 0 0 8) a f 9 8 0 9 SI 8 8 0 0 Q 9 0 0 ! o. 1 1 ! i 0 50 10o 15Q LOGNORMAL EXPECTED: * OBSERVED: o 80 0 O 9 9 9 O * 9 9 O * 9 9 O * e 9 O * 9 8 9 40 9 9 9 9 9 9 9 9 O * 9 9 9 9 9 * 9 9 9 9 8 * 9 9 9 8 9 o 9 9 9 9 9 9 9 O 9 9 9 9 9 9 8 s 9 9 9 9 9 9 9 9 O 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 8 8 9 * 8 50 100 AIRPORT A, 1981 NORMAL OBSERVED- o : EXPECTED- e : VARIABLE (.COLUMN NO.) 1 150| 100 50 O O O o e o 0 o 0 « e • « 9 0 0 0 0 0 0 0 O 0 0 0 I 50 100 0 0 o o 0 0 0 0 I 150 I® 0 I 200 POISSON OBSERVED- O : EXPECTED- 0 : VARIABLE (COLUMN NO. ) 1 150| 100 50 0 O 0 9 0 0 0 0 0 0 0 0 » 0 50 0 9 0 O 0 0 O O O O O O O O I 100 o o 0 O o o o O 0 0 0 |o o 150 200 LOGNORMAL EXPECTED: * 150 OBSERVED: o AIRPORT B, 1978 OBSERVED-0 : EXPECTED-a : iv/l/ET̂ BI/T (COLUMN NO.) 1 100 1 o 1 o o 75| 0 0 o a | 0 o a o a ] o e a o a j o o ® a o a j o 9 a a o a a 50| o o a a a o a a | o a a a a o a 0 a | o a ® a a o 0 o 0 a | 0 0 o a a | o o 0 a o o 25 | o o 0 a o a o | 0 o o a o a o j o 0 o a o a a o |9 e 0 8 8 8 8 8 a o 0 o 0 a o a a a o o o 0 |0 o 1 1 1 1 1 1 10 1 1 0 50 100 150 200 250 OBSERVED-O : EXPECTED-a : VARIABLE (COLUMN NO.) 1 100| | a j a a a j o a a | o o e a a 751 o a o a a a | o a o 0 a a | o a o 0 a a I o o e o o a a a | o a a 0 o a a a 50| o o a a o o a a a | o o a a o o a a 0 a | o o a a o 0 o 0 p a I o a a a o o o o o a I o a a a o o o 0 o a a o 25| 0 o a a a o 0 0 o o a a o o 1 o a a a a o o o o o a a a o I o a a a a o o 0 o o a a a o o j 0 o o o o a a a a o | o 0 o 0 0 9 O 0 |e « 1 1 1 1 1 1 a|a | 1 0 50 100 15o 2C0 250 LOGNORMAL EXPECTED: * OBSERVED: o 100 O * * O * 9 : : O 50 ; : : : ': : : * O O a a a 8 9 8 * BOO a s a 9 9 8 9 9 8 O 9 9 9 8 9 3 9 9 9 0 O O 9 9 9 9 3 8 9 8 9 8 8 o o 9 9 9 9 9 3 8 8 9 9 9 9 O o 9 3 9 9 9 9 9 9 3 9 3 9 9 O * 9 3 9 9 9 9 9 9 S 9 8 ' 8 9 « 8 * 9 9 9 9 9 9 9 9 3 9 8 9 8 9 8 9 8 8 * a a 3 9 3 9 9 8 9 9 9 9 9 9 3 9 9 9 9 9 9 50 100 150 200 120 AIRPORT B, 1979 NORMAL OBSERVED- o : EXPECTED- « : VARIABLE (.COLUMN NO.) 1 1001 oo oe«® 75| 0 9 9 9 o 9 9 9 0 0 0 ® 9 9 ® 0 0 9 501 0 9 9 9 9 0 0 9 0 9 9 9 9 0 0 9 9 9 9 9 9 0 0 9 9 9 9 9 9 9 0 0 9 0 9 9 9 9 9 O O 0 O j c 25| < | 9 < 9 9 9 9 9 9 0 0 0 0 9 0 3 9 9 9 9 9 9 0 0 0 0 9 0 B 9 9 9 9 9 9 0 0 0 0 9 9 B 9 9 9 9 9 9 0 O O 0 9 9 0 O I ocx o| 0 100 200 300 OBSERVED-o : EXPECTED- 9 : VARIABLE (COLUMN NO.) 1 100 i 9 9 9 0 0 0 9 9 50| 0 0 9 0 0 0 0 9 0 9 9 0 0 0 0 9 9 9 9 0 0 0 0 0 9 9 0 0 9 9 9 0 0 0 0 0 9 0 0 0 9 9 9 9 0 0 0 0 0 9 0 9 * w 0 1 0 0 9 9 9 9 9 0 0 0 0 0 9 0 9 8 9 9 | | | 100 >90 200 30 0 . LOGNORMAL EXPECTED: * OBSERVED: o 100 9 9 * 9 9 O * 9 9 9 * 9 9 9 O B O 9 O 50 lr O o O O o 0 * 100 200 121 AIRPORT B, 1980 NORMAL OBSERVED-o : EXPECTED-0 : VARIABLE (COLUMN NO.) 1 75| | o o | o j o 50| o 0 0 9 0 | o o 0 O 0 O 0 0 | 0 o 0 O 0 O 0 0 | 0 9 0 O 0 O 0 O 0 j o 9 0 o O 0 0 0 O 0 0 25| • o 0 9 0 O 0 o o O O O 0 | 0 8 0 e o O 0 o 0 O O 0 o j 9 e e e 0 o O 0 o 0 O O O O 0 o o | a e e e 0 o o O 9 0 O O O O O 0 0 O O | O O 9 9 0 o o O 9 o 0 O O O O 0 0 0 0 O 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 50 100 150 200 250 OBSERVED-o ; EXPECTED-0 : VARIABLE {COLUMN NO.) 1 IS] 1 o 1 0 0 1 0 0 0 0 50| o 9 0 0 0 0 0 0 1 o o 0 O 9 O 0 e 1 o o 0 O 0 o o o © 1 O 0 0 O 0 o o O 0 1 O O 0 O O 0 o o O 9 0 25| O O 0 o O 0 o o o o o 1 O O 0 0 o O 0 o o o O 0 « 1 O O 0 0 o O 0 o o o o o « ) O O 0 1 0 0 0 0 o O 0 o 0 o o o « ) 0 0 O 0 1 O O 0 0 0 0 o O 9 o o 0 o o « > O 0 0 0 O 0 01 0 0 | | 1 1 1 1 1 9 e | 0 50 100 150 200 250 LOGNORMAL EXPECTED: * OBSERVED: O 80 122 AIRPORT B, 1981 NORMAL OBSERVED-o : EXPECTED-9 : VARIABLE (COLUMN NO.) X ISO] | O 100 I o 1 0 ® 1 o 9 9 9 9 9 j. o 0 o 9 O 9 O 9 1 0 0 9 O O 9 O O 9 50 | o 9 9 O O 9 O O 9 9 O | 9 0 9 9 9 O O 9 O O 9 9 9 j 9 9 9 9 9 o o 9 O O 9 9 9 9 j 9 9 9 9 9 o o 9 0 0 9 9 9 9 9 0 j O 9 9 9 9 O 0 9 0 0 9 9 9 9 9 9 9 O ol 1 1 1 1 1 1 | 9 9 | 9 | 1 0 50 100 150 200 250 POISSON OBSERVED-o : EXPECTED-9 : VARIABLE (COLUMN NO.) 1 ISO] o 9 9 9 9 100 I o 9 9 9 1 o 9 9 O 9 9 1 o 9 9 O 9 9 1 0 o o 9 O O 0 9 9 1 O O 9 O O O o O O 50| O O 9 O O O O O O 9 O | o 0 9 © O O O O O O 9 O j o O 9 9 O O o O O O 9 9 O j o 9 9 9 O O o 0 0 0 9 9 9 0 0 j O 9 © 9 9 o o o 0 0 0 9 9 9 9 9 0 0 01 9 | 1 1 | | | 9 9 9|9 | 1 0 50 100 150 200 250 LOGNORMAL EXPECTED: * OBSERVED: o 150 AIRPORT B, 1982 123 - ...... OBSERVED-0 : EXPECTED- 9 : VARIABLE {COLUMN NO.) 1 100 I I o 0 I o o o I o o e 9 I o 0 9 O 9 75| o 9 9 0 9 1 o 9 9 o 9 I 9 0 9 o 9 9 I 9 e 9 o 9 9 I O 9 9 9 o 9 0 50| O 0 0 9 0 9 0 0 I 0 0 0 0 o O 0 0 1 9 © 0 0 o O o 0 1 9 e 0 9 o O O 0 1 9 9 9 0 9 o O. O 9 0 25 I 9 9 9 9 9 o O O 9 O 1 9 0 9 9 9 9 o O O 9 O 9 1 O O « 9 0 9 o O O 9 O 9 o 1 9 9 O 0 9 0 9 9 0 O O 9 0 0 0 1 9 o o 0 9 9 0 9 o o O 9 0 0 0 0 0 1 0 1 1 1 | 9 9|0 0 | 1 0 50 100 150 200 250 0BSERVED-o : EXPECTED- 0 : VARIABLE (COLUMN NO.) 1 100! | o O j o o o j o O 0 9 j o O 0 O 75| o 0 O 0 I 0 0 O 0 1 o 0 O 0 0 j 9 0 O 0 9 1 O 9 0 O 9 o 50| O 0 9 O 0 0 0 1 9 0 0 O 0 0 0 1 9 0 9 O o o 9 1 9 0 0 O o o 9 9 I 9 0 9 O o o 0 0 25| 9 0 0 0 O o o 9 O 9 I O 0 0 9 o o o 0 O O • 1 9 O 9 9 9 0 o o 0 O O 0 1 9 O 9 9 9 0 0 0 0 O O 0 9 I 9 9 O 8 0 9 o o 0 0 O O 9 O 9 9 0 1 9 | | 1 | | O O I> 9 | 1 0 50 '100 15° 200 250 LOGNORMAL EXPECTED: * OBSERVED: o 100 O O O i l I I : : : * O 9 8 9 9 9 9 * 0 50 9 8 8 9 9 9 8 8 O 8 9 8 5 8 9 8 8 0 9 8 8 9 8 9 8 9 O * 9 0 ! , 9 9 9 9 9 O r '. 9 9 8 6: 9 9 9 9 8 8 8 O 9 9 9 S 9 9 9 3 9 9 3 9 o 9 8 9 9 ? 9 9 9 9 9 9 9 9 9 o 9 3 9 9 S 9 3 9 3 9 9 9 9 8 8 9 9 9 8 9 8 5 9 9 9 9 8 9 3 9 9 9 9 9 9 8 50 " " " " " l o o '""150""" 200 124 AIRPORT C, 1980 •- -- - OBSERVED-o : EXPECTED-e : VARIABLE (COLUMN NO.) 1 ISO] | 0 j O 9 j 9 9 100 | O 9 O 1 0 9 O 9 1 9 9 0 9 1 9 9 0 9 1 9 9 0 9 50 1 9 9 0 9 9 | 9 9 9 O 9 O | O 9 9 O 9 O j s 0 9 9 0 9 0 9 j 9 0 9 9 O 9 O 9 9 o| O 1 1 1 . |9 9 9 | 0 50 100 150 POISSON OBSERVED-o EXPECTED-9 : VARIABLE (COLUMN NO.) 1 ISO I | O j O | O 100 I o O O 1 0 9 9 O 1 o 9 9 9 J a 9 9 9 50 | | 9 | o 9 9 9 9 O 9 j 9 o 9 9 9 9 O O 9 | 9 o 9 9 9 9 O O O 9 9 ol o 1 1 - 1 •|0 O 9- | 0 50 100 150 LOGNORMAL EXPECTED: * OBSERVED: o 150 9 9 9 9 * 9 9 50 100 AIRPORT C, 1981 125 NORMAL POISSON OBSERVED-o : EXPECTED-® : VARIABLE (COLUMN NO.) 1 200| I O I 0 1 o 150| 9 9 9 | o 9 O | o 9 O | o 9 O | 9 9 O . 100 I 9 9 O 9 1 9 9 O 9 | 9 9 O O | 9 9 O O j 9 9 9 O O 50| O 9 9 O O 9 I O 9 9 O O 9 I O 9 9 O O O I 9 O 9 9 O O O 0 | 9 O 9 9 O O O 9 O 01 o 1 1 1 «|9 | | 0 50 100 150 OBSERVED-o : EXPECTED-9 : VARIABLE (COLUMN NO.) 1 2001 | o j o | o | o 1501 0 | o O 0 j o o o | o 9 9 | o 9 9 100 I 9 9 9 9 9 1 9 9 9 O 1 9 9 9 O 9 1 9 9 9 9 O 9 501 O 9 9 9 O 9 | O 9 9 9 O 9 9 | 9 O 9 9 9 O O 9 | 9 O 9 9 9 O O O 9 9 | 9 O 9 9 9 O O O O 9 0 1 o I 1 1 |o | | 0 50 100 150 LOGNORMAL EXPECTED: * OBSERVED: 200 o * 9 9 9 0 100 9 « 9 9 9 » 9 9 9 O 9 9 « 50 100 126 AIRPORT G, 1981 OBSERVED- o : EXPECTED- ® : VARIABLE (COLUMN 110.) 1 150 | 1 o 1 o 100 i o 1 o oo j oo ®A®® |® 0090®®®00®® 50|® 0®ec | v www. >®eeoo®®e >®e®oooo®® BulUnA/WV̂/VB I®oe®®o®®eooooooo®®o | ®0®®«0®®»0000000®Se8000 0 |o | 1 1 | » « ® I | 0 100 200 300 POISSON OBSERVED - o : EXPECTED- e : VARIABLE (.COLUMN NO.) l' 150| ] 9 | o «ee j O 9®®9 100| o ®®®®® 1 o eoo®9® j oo ®oo®«® 1 ooooooooo®® so | oooooooooae 1 ooeoooooooo® 1 00*000000000® j 009900000000099000 1 o®®®ooooooooo®®90ooooo 0 |« »e I | | as®®®» | | 0 100 200 300 LOGNORMAL EXPECTED: * OBSERVED: o L50 AIRPORT G, 1982 OBSERVED- o : EXPECTED- a : VARIAB :,E (COLUMN HO.) 1 100 I 1 o 1 0 I oo 0 9 9 9 75| 0 0 0 9 9 0 9 9 0 0 9 9 9 0 0 9 9 0009990009 1® 50 |® oo®«e®oooo® 0 0 9 9 9 9 0 0 0 0 9 o®®a«®oooo®® 1* oeeeeaooooe® |8 ©®&©®&ooooo®© 1® 8 9 9 9 9 9 0 0 0 0 0 9 9 |s« 8 9 9 9 9 9 9 0 0 0 0 0 0 0 9 0 25 |9« 6 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0 |9C aaaaaaaooooooooe jec 3®®®®a®oooooooo®® o |oc 3®ae«aaooooooooaeo®aoo 0 1 1 1 1 | 9®9| 1 0 100 200 300 POISSON OBSERVED-o : EXPECTED- 9 : VARIABLE (COLUMN NO.) 1 150| 9 999 100 I a a a ® a o ®aa®a | O 009999 | 009000999 | 009000009 j 00090000009 50| 00090000009 | 009900000009 | ooaaooooooooooo | 00999000000009000 0 j oeaaeooooooooaeaooooo 0|a 9 | | | 8998999| J 0 100 200 300 LOGNORMAL EXPECTED: * OBSERVED: o 150

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
China 10 23
Japan 3 0
United Kingdom 2 0
United States 1 1
City Views Downloads
Beijing 10 0
Tokyo 3 0
Belper 2 0
Ashburn 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}

Share

Share to:

Comment

Related Items