Input modeling for discrete distributions

Abstract

In this thesis we developed a new input modeling tool called FitAllDiscrete(x) for the statistical software R. We then tested the success of our modeling tool by comparing it with two popular commercial softwares: Arena input analyzer and EasyFit. Considering limitations of the software packages we mention, we developed a more powerful tool which is based on well-accepted and e cient statistical methods. Input modeling tools model the data to nd the most proper distribution. Our input modeling function considers input data from discrete distributions. It tries all distributions automatically and recommends the most proper one for the data. Input modeling is executed by the three essential steps including distribution selection, parameter estimation and goodness of t testing. In this study, for distribution selection we used Akaike's information criterion (AIC) which is a popular selection criterion. For parameter estimation we used maximum likelihood estimation (MLE). Akaike's information criterion does not guarantee that the selected distribution has a good t for the data. Therefore, we applied the chi-square test to assess whether the t is statistically meaningful. According to it, if the t is good the distribution is accepted and recommended to the user. Otherwise, the empirical distribution is recommended. To decide how reliable our tool is, we rst performed an automatic test. Then, we performed a manual test by comparing our input modeling tool with Arena input analyzer and EasyFit. During the tests, we used random discrete data sets generated from the distributions of our pool. The results of the automatic test showed that our input modeling tool is successful in nding the correct distributions for simulated data sets. The comparison test showed that the recommendations by FitAllDiscrete(x) are more successful than those of the commercial products. Hence we succeeded in developing a new high-quality input analyzer.