The effect of dependence on distribution of the functions of random variables |
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Authors: | Ali Dolati Najmeh Ahmadi Zohreh Shishebor |
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Affiliation: | 1. Department of Statistics, Yazd University, Yazd, Iran;2. Department of Statistics, Shiraz University, Shiraz, Iran |
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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. |
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Keywords: | Copula Dependent random variables Distribution of sums Stress–strength measure Value-at-risk. |
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