Generalized location-scale mixtures of elliptical distributions: Definitions and stochastic comparisons

Pu, Tong1,2; Zhang, Yiying1; Yin, Chuancun2,3

2023

10.1080/03610926.2023.2165407

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS   Impact Factor & Quartile

0361-0926

1532-415X

This article proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector Z, independent of X and Y, the scale parameter of this class of distributions is mixed with a function alpha(Z) and its skew parameter is mixed with another function beta(Z). Sufficient (and necessary) conditions are established for stochastically comparing different random vectors stemming from this class of distributions by means of several stochastic orders including the usual stochastic order, convex order, increasing convex order, supermodular order, and some related linear orders. Two insightful assumptions for the density generators of elliptical distributions, aiming to control the generators' tail, are provided to make stochastic comparisons among mixed-elliptical vectors. Some applications in applied probability and actuarial science are also provided as illustrations on the main findings.

Asymmetric distributions elliptical distribution integral stochastic orderings location-scale mixture skew-normal distributions

SCI

English

First

National Natural Science Foundation of China["12101336","12071251"]

Mathematics

Statistics & Probability

WOS:000921815600001

TAYLOR & FRANCIS INC

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen, Guangdong, Peoples R China
2.Qufu Normal Univ, Sch Stat & Data Sci, Qufu, Shandong, Peoples R China
3.Qufu Normal Univ, Sch Stat & Data Sci, Qufu 273165, Shandong, Peoples R China

Pu, Tong,Zhang, Yiying,Yin, Chuancun. Generalized location-scale mixtures of elliptical distributions: Definitions and stochastic comparisons[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS,2023.

Pu, Tong,Zhang, Yiying,&Yin, Chuancun.(2023).Generalized location-scale mixtures of elliptical distributions: Definitions and stochastic comparisons.COMMUNICATIONS IN STATISTICS-THEORY AND METHODS.

Pu, Tong,et al."Generalized location-scale mixtures of elliptical distributions: Definitions and stochastic comparisons".COMMUNICATIONS IN STATISTICS-THEORY AND METHODS (2023).