The distribution of the sum of two dependent randomly weighted random variables with applications

Rasool Roozegar, Abdolsaleh Toghdori and Saralees Nadarajah

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 6, 1985-2002

Abstract: There has been much work on the distribution of independent or dependent random variables. But we are not aware of any work giving exact results for the distribution of the sum of randomly weighted random variables. In this paper, we derive exact results for the randomly weighted sum of two dependent random variables. The derived expressions are for the cumulative distribution function, conditional expectation, moment generating function, value at risk, expected shortfall and the limiting tail behavior of the randomly weighted sum of two dependent random variables. Two numerical illustrations are given.

Date: 2024
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DOI: 10.1080/03610926.2022.2117558

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