A novel unit-asymmetric distribution based on correlated Fr\'echet random variables

TL;DR

This paper introduces a new unit-interval distribution derived from correlated Fréchet variables, analyzing its properties and applications, providing a novel tool for modeling extreme value phenomena.

Contribution

It proposes a new ratio-based distribution from correlated Fréchet variables and thoroughly analyzes its mathematical properties and potential applications.

Findings

Distribution characterized as a ratio of correlated Fréchet variables.

Mathematical properties including moments and stress-strength probability derived.

Applications demonstrating the distribution's practical utility.

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 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.