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arXiv · 2408.00100

A new unit-bimodal distribution based on correlated Birnbaum-Saunders random variables

Roberto Vila·Helton Saulo·Felipe Quintino·Peter Zörnig
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Abstract

In this paper, we propose a new distribution over the unit interval which can be characterized as a ratio of the type $Z=Y/(X+Y)$ where $X$ and $Y$ are two correlated Birnbaum-Saunders random variables. The density of $Z$ may be unimodal or bimodal. Simple expressions for the cumulative distribution function, moment-generating function and moments are obtained. Moreover, the stress-strength probability between $X$ and $Y$ is calculated explicitly in the symmetric case, that is, when the respective scale parameters are equal. Two applications of the ratio distribution are discussed.

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Roberto Vila, Helton Saulo, Felipe Quintino, Peter Zörnig. 2024-07-31. A new unit-bimodal distribution based on correlated Birnbaum-Saunders random variables. https://arxiv.org/abs/2408.00100

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