In this paper, we propose a new distribution with unitary support which can be characterized as a ratio of the type $W=X_1/(X_1+X_2)$, where $(X_1, X_2)^\top$ follows a bivariate extreme distribution with Fr\'echet margins, that is, $X_1$ and $X_2$ are two correlated Fr\'echet random variables. Some mathematical properties such as identifiability, symmetry, stochastic representation, characterization as a ratio, moments, stress-strength probability, quantiles, and the maximum likelihood method are rigorously analyzed. Two applications of the ratio distribution are discussed.

翻译：本文提出了一种具有单位支撑的新分布，该分布可表征为 $W=X_1/(X_1+X_2)$ 形式的比率，其中 $(X_1, X_2)^\top$ 服从具有Fréchet边缘的二元极值分布，即 $X_1$ 和 $X_2$ 是两个相关的Fréchet随机变量。我们严格分析了该分布的一些数学性质，包括可识别性、对称性、随机表示、比率表征、矩、应力-强度概率、分位数以及极大似然估计方法。文中还讨论了该比率分布的两个应用实例。