Goodness of fit test for logistic distribution involving Kullback-Leibler information (Ujian kebagusan penyuaian untuk taburan logistik menerusi maklumat Kullback-Leibler)

Abstract

In this paper, our objective is to test the statistical hypothesis : ( ) ( ) for all against : ( Ho F x  F o x x H1 F x)  Fo (x) for some x , where F o (x ) is a known distribution function. In this study, a goodness of fit test statistic for testing the logistic distribution based on Kullback-Leibler information as proposed by Song (2002) is studied. The logistic parameters are estimated by using several methods of estimation such as maximum likelihood, order statistics, moments, L-moments and LQ-moments. The critical value based on the statistics which involves the Kullback-Leibler information under the assumption that Ho is true is computed using Monte Carlo simulations. The performance of the test under simple random sampling is investigated. Ten different distributions are considered under the alternative hypothesis. Based on Monte Carlo simulations, for all the distributions considered, it is found that the test statistics based on estimators found by moment and LQ-moment methods have the highest power, except for Weibull (2, .5) and Gamma distributions