ON TESTING THE ADEQUACY OF THE GUMBEL MODEL WITH APPLICATION TO COVID-19 DATA

Abstract

The Gumbel distribution is one of the most used models to carry out risk analysis in extreme events, in reliability tests, and in life expectancy experiments. In this article, we propose a goodness of fit test for the Gumbel distribution based on a new estimate of Kullback-Leibler information. The properties of the test statistic are presented. In order to compute the proposed test statistic, the unknown parameters of the Gumbel distribution are estimated by the maximum likelihood method. Critical points of the proposed test statistic are obtained by Monte Carlo simulation. Through a simulation study, power values of the proposed test are computed and then compared with some prominent existing tests. Finally, two real data examples are presented and analyzed.