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UBC Theses and Dissertations

Statistical transformation of probabilistic information Lee, Moon Hoe

Abstract

This research study had shown various probable rational methods of quantifying subjective information in a probability distribution with particular reference to the evaluation of economic projects by computer simulation. Computer simulation to give all the possible outcomes of a capital project using the Monte Carlo technique (method of statistical trials) provides a strong practical appeal for the evaluation of a risky project. However, a practical problem in the application of computer simulation to the evaluation of capital expenditures is the numerical quantification of uncertainty in the input variables in a probability distribution. One serious shortcoming in the use of subjective probabilities is that subjective probability distributions are not in a reproducible or mathematical form. They do not, therefore, allow for validation of their general suitability in particular cases to characterize input variables by independent means. At the same time the practical derivation of subjective probability distributions is by no means considered an easy or exact task. The present study was an attempt to suggest a simplification to the problem of deriving a probability distribution by the usual method of direct listing of subjective probabilities. The study examined the possible applicability of four theoretical probability distributions (lognormal, Weibull, normal and triangular) to the evaluation of capital projects by computer simulation. Both theory and procedures were developed for employing the four theoretical probability distributions to quantify the probability of occurrence of input variables in a simulation model. The procedure established for fitting the lognormal probability function to three-level estimates of probabilistic information was the principal contribution from this study to research in the search for improved techniques for the analysis of risky projects. A priori considerations for studying the lognormal function were discussed. Procedures were also shown on how to apply the triangular probability function and the normal approximation to simulate the outcomes of a capital project. The technique of fitting the Weibull probability function to three-level estimates of forecasts was adopted from a paper by William D. Lamb. The four theoretical probability functions wore applied to a case problem which was analyzed using subjective probabilities by David B. Hertz and reported in the Harvard Business Review. The proposal considered was a $10/-million extension to a chemical processing plant for a medium-sized industrial chemical producer. The investigations of the present study disclosed that the log-normal function showed considerable promise as a suitable probability distribution to quantify the uncertainties surrounding project variables. The normal distribution was also found to hold promise of being an appropriate distribution to use in simulation studies. The Weibull probability function did not show up too favourably by the results obtained when it was applied to the case problem under study. The triangular probability function was found to be either an inexact or unsuitable approximation to use in simulation studies as shown by the results obtained on this case problem. Secondary investigations were conducted to test the sensitivity of Monte Carlo simulation outputs to (l) number of statistical trials; (2) assumptions made on tail probabilities and (3) errors in the three-level estimates.

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