Goodness of Fit Test for Gumbel Distribution Based on Kullback-Leibler Information Using Several Different Estimators

In this paper, our objective is to test the statistical hypothesis : ( ) ( ) for all against : ( ) ( ) 1 H F x F x x H F x F x o o o = ≠ for some , x where ( ) F x o is a known distribution function. In this study, a goodness of fit test statistics for Gumbel distribution based on Kullback-Leibler information is studied. The performance of the test under simple random sampling is investigated using Monte Carlo simulation. The Gumbel parameters are estimated by using several methods of estimation such as maximum likelihood, order statistics, moments, and L-moments. Ten different distributions are considered under the alternative hypothesis. For all the distributions considered, it is found that the test statistics based on estimators found by moment and order statistic methods have the highest power, except for weibull and Lognormal distributions.