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

2023/07/13 by Vila, Roberto, Balakrishnan, Narayanaswamy, Bourguignon, Marcelo · 1 citation
#60E05 #62Exx #62Fxx #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2307.06817

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 \stackreld= 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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