Kolmogorov goodness-of-fit test for S-symmetric distributions in climate and weather modeling

Abstract

Statistical data treatment is an essential part of climate and weather modeling. The Kolmogorov goodness-of-fit test is a widely applicable statistical method to determine the cumulative distribution function of a continuous random variable, e.g., a precipitation level, wind force, etc. In this paper, the authors consider a problem of goodness-of-fit testing involving additional information about S-symmetry of the cumulative distribution function and its influence on the Kolmogorov statistic distributions. A definition of S-symmetry is given; it is a generalized classical definition of distribution symmetry. It is proved that any continuous increasing cumulative distribution function is S-symmetric. A uniform distribution is considered as an example of an S-symmetric distribution. A modification of the Kolmogorov statistic using additional information about the new type of symmetry is proposed. The exact and asymptotic distributions under the null and the alternative hypothesis of the modified statistics are described. The authors also provide an example which proves that the modified test is more powerful than the non-modified one. The new test is used to check the hypothesis of a uniform distribution of the average sum of precipitation.