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

In this paper, we propose a new distribution over the unit interval which can be characterized as a ratio of the type Z=dY/(X+Y)$$Z{\mathop {=}\limits ^{d}}Y/(X+Y)$$ 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.