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Estimating mixtures of exponential distributions using maximum likelihood and the EM algorithm to improve simulation of telecommunications networks Baird, Sean Robert

Abstract

This thesis explores the topic of mixture-distributions as they relate to modeling call demand on a telecommunications network. Modeling call duration demand in particular proves difficult for a number of reasons. Historically, this has been modeled using a simple exponential distribution with a single parameter. This work extends that modeling technique to using multi-component exponential distributions. Development of these models is shown to be possible using non-linear programming as well as an application of the EM algorithm. These independent approaches yield remarkably similar results. Also relevant are the treatment of statistical significance testing for large data set samples, since these notoriously pose difficulty by magnifying statistical significance. This problem is treated through a more robust comparison of data to the theoretical distribution using a bootstrapping technique of sampling against the large data set. Finally, the results of the demand modeling are also validated using a more intuitive comparison to the simulation model output.

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