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arXiv · 2307.06817

On the distribution of a random variable involved in an independent ratio

Roberto Vila·Narayanaswamy Balakrishnan·Marcelo Bourguignon
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Abstract

In this paper, using inverse integral transforms, we derive the exact distribution of the random variable $X$ that is involved in the ratio $Z \stackrel{d}{=} X/(X+Y)$ where $X$ and $Y$ are independent random variables having the same support, and $Z$ and $Y$ have known distributions. We introduce new distributions this way. As applications of the obtained results, several examples are presented.

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Roberto Vila, Narayanaswamy Balakrishnan, Marcelo Bourguignon. 2023-07-13. On the distribution of a random variable involved in an independent ratio. https://arxiv.org/abs/2307.06817

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