On application of the univariate Kotz distribution and some of its extensions

Abstract

Despite a flourishing activity, especially in recent times, for the study of flexible parametric classes of distributions, little work has dealt with the case where the tail weight and degree of peakedness is regulated by two parameters instead of a single one, as it is usually the case. The present contribution starts off from the symmetric distributions introduced by Kotz in 1975, subsequently evolved into the so-called Kotz-type distribution, and builds on their univariate versions by introducing a parameter which allows for the presence of asymmetry. We study some formal properties of these distributions and examine their practical usefulness in some real-data illustrations, considering both symmetric and asymmetric variants of the distributions.