A goodness-of-fit test for maximum order statistics from discrete distributions

In economic, financial and environmental sciences studies the extreme value theory is used for the evaluation of several complex occurring phenomena, e.g., risk management theory, natural calamities, meteorology and pollution studies. When the observed values are discrete, like count measurements, the discrete extreme value distributions should be applied. In this paper we propose a procedure to evaluate the goodness of fit of extreme values from discrete distributions. In particular we modify the classic statistic of the Kolmogorov-Smirnov goodness of fit test for continuous distribution function. This modification is necessary since the assumption of the Kolmogorov-Smirnov test is the continuity of the distribution specified under the null hypothesis. The distribution of the proposed test is given. The exact critical values of the test statistic are tabulated for extreme values from some specific discrete distributions. An application in environmental science is presented.