On connections between skewed, weighted and distorted distributions: applications to model extreme value distributions

Jorge Navarro () and Jorge M Arevalillo
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Jorge Navarro: Universidad de Murcia
Jorge M Arevalillo: UC3M-Santander Big Data Institute

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 4, No 11, 1307-1335

Abstract: Abstract The purpose of the paper is to explore the connections between skew symmetric, weighted and distorted univariate distributions as well as how they appear related to the distributions of the extreme values in a sample of identically distributed random variables under both the independence and dependence scenarios. Some extensions of the concept of skewed distributions are proposed in order to cover the most general cases of extremes. Their natural connections to the likelihood ratio ordering and the role played by the P–P plots for handling these models are also highlighted. The results can also be applied to order statistics and coherent systems although these cases do not always lead to skewed distributions. The theoretical findings are illustrated by applied examples to model extremes as well as by several applications concerned with the analysis of artificial and real data.

Keywords: Skewness; Distortions; Order statistics; Copula; 60E15; 62N05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-023-00874-x

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