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.

翻译：本文提出了一种定义在单位区间上的新分布，该分布可表征为$Z=Y/(X+Y)$形式的比率，其中$X$和$Y$是两个相关的Birnbaum-Saunders随机变量。$Z$的密度函数可能呈现单峰或双峰形态。我们推导出了其累积分布函数、矩母函数及各阶矩的简洁表达式。此外，在对称情形（即两个随机变量的尺度参数相等）下，显式计算了$X$与$Y$之间的应力-强度概率。最后探讨了该比率分布的两个应用场景。