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

TL;DR

This paper introduces a novel unit-bimodal distribution derived from correlated Birnbaum-Saunders variables, providing explicit formulas and applications, expanding the modeling tools for correlated random variables on the unit interval.

Contribution

It proposes a new ratio-based distribution on the unit interval from correlated Birnbaum-Saunders variables, with explicit formulas and practical applications.

Findings

Distribution can be unimodal or bimodal.

Explicit formulas for CDF, MGF, and moments.

Applications in stress-strength analysis.

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.