On application of the univariate Kotz distribution and some of its extensions
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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.
KeywordsKotz-type distribution Peakedness Perturbation of symmetry Skew-symmetric distributions Symmetry-modulated distributions Tail-weight parameter Two-sided generalized Gamma distribution
We thank an anonymous reviewer for a set of comments to an earlier version of the paper, leading to a better presentation of the material. This work was started when the first author was visiting the Department of Statistical Sciences, University of Padua, Italy, and completed while he was at the Ferdowsi University of Mashhad, Iran; the support of these institutions is gratefully acknowledged. We are grateful to Francesco Lisi for kindly providing the S&P data.
- 3.Azzalini, A.: The R package sn: The Skew-Normal and Skew-t distributions (version 1.3-0). (2015). http://azzalini.stat.unipd.it/SN
- 4.Azzalini, A., With the collaboration of Capitanio, A.: The Skew-Normal and Related Families. IMS monographs. Cambridge University Press, Cambridge (2014)Google Scholar
- 6.Bowman, A. W., Azzalini, A.: The R package sm: nonparametric smoothing methods (version 2.2-5.4). University of Glasgow, UK and Università di Padova, Italia (2014)Google Scholar
- 9.Gilbert, P., Varadhan, R.: The R package numDeriv: Accurate Numerical Derivatives (version 2014.2–1) (2015). https://CRAN.R-project.org/package=numDeriv
- 15.Mullen, K., Ardia, D., Gil, D., Windover, D., Cline, J.: DEoptim, An R package for global optimization by differential evolution. J. Stat. Softw. 40(6) (2011). http://www.jstatsoft.org/v40/i06/
- 18.R Core Team, R.: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2017). https://www.R-project.org/.