Input modeling

Abstract

In this study input modeling is executed by using the most e cient statistical principles and a new input modeling tool, the Fit All function, is developed in the statistical computing environment R. Moreover a practical comparison between this function and commercial input modeling softwares such as the Arena Input Analyzer and EasyFit is made. The Fit All function automatically tries all distributions for the input data and recommends the most proper model to the user. Twenty- ve continuous distributions are included to this function and the maximum likelihood method (MLE) is utilized to estimate the parameters for all these distributions. For model selection, Akaike's Information Criterion (AIC) is used which is a theoretically sound and popular criterion for model selection. The main advantage of utilizing AIC is that it is based on calculating the log-likelihood of the candidate distribution, therefore it is consistent with the MLE. To assess the goodness of t for the best tting distribution, the Chi-Square test is executed. If a proper t can be found, this model is recommended to the user. Otherwise the empirical model is recommended. To compare the models recommended by the Fit All function, the Arena Input Analyzer and EasyFit; random samples from common distributions are generated. The results of the simulation study show that the Fit All function identi es the correct distribution clearly more successfully than the other softwares. This means that AIC performs much better than the other model selection procedures. Moreover the parameter estimates that are presented by the Fit All function are closer to the original parameters. This also shows that the MLE obtains high quality parameter estimates.