A novel unit-asymmetric distribution based on correlated Fréchet random variables

Abstract

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 Fréchet margins, that is, $X_1$ and $X_2$ are two correlated Fréchet 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.

24 pages, 10 figures