Skewed Kotz Distribution with Application to Financial Stock Returns

  • Abdellatif Bellahnid
  • Amadou SarrEmail author
Original Article


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.


Kotz distribution Skewed T distribution Skewed Kotz distribution Financial returns Value-at-risk Average value-at-risk Excess kurtosis 

Mathematics Subject Classification

62E15 62P05 



The authors thank the editor and anonymous referees for their very valuable suggestions and comments that improved the presentation of the paper.

Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, I (Amadou Sarr, corresponding author) state that there is no conflict of interest about our manuscript.


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Copyright information

© Grace Scientific Publishing 2019

Authors and Affiliations

  1. 1.Department of StatisticsSultan Qaboos UniversityMuscatOman

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