Skewed Kotz Distribution with Application to Financial Stock Returns

Abstract

This paper introduced a five-parameter skewed Kotz (SK) distribution that may be viewed as a generalized skewed T distribution. Its mathematical properties are investigated, and parameters are estimated using the maximum likelihood method. The usefulness of this new distribution has been illustrated by deriving explicit formulae for the value-at-risk (VaR) and the average value-at-risk (AVaR). The obtained results are clearly generalizations of those that were established earlier by Dokov et al. (J Appl Funct Anal 3(1):189–208, 2008). On the other hand, simulation studies have been conducted and showed the accuracy of the VaR and AVaR computations. Furthermore, an application on financial returns of the Universal Health Services stock provided evidence that the SK distribution better fits the empirical distribution than both normal and skewed T distributions. The empirical study revealed the suitability of the SK distribution, specially for modelling data that fall within a small range, with a high excess kurtosis.