The effect of dependence on distribution of the functions of random variables. Issue 21 (2nd November 2017)

• Record Type: Journal Article
• Authors: Dolati, Ali; Roozegar, Rasool; Ahmadi, Najmeh; Shishebor, Zohreh
• Is Part Of: Communications in statistics. Volume 46:Issue 21(2017)
• Page Start: 10704
• Page End: 10717
• Publication Date: 2017-11-02
• Subjects: Copula -- Dependent random variables -- Distribution of sums -- Stress–strength measure -- Value-at-risk.; 60E05 -- 62E15; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2016.1242740
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this article, we study the effect of dependence on the distributional properties of functions of two random variables. Expressions for the cumulative distribution functions of the linear combinations, products, and ratios of two dependent random variables in terms of their associated copula are derived. We discuss the effect of dependence on quantities such as the variances of linear combinations of functions, the value-at-risk measure, and the stress–strength parameter. Several examples, a simulation study, and a real data analysis are provided to illustrate the result.