Estimation of P(X < Y) stress-strength reliability measures for a class of asymmetric distributions : the case of three-parameter p-max stable laws - Quintino, Felipe Sousa (2024)
Asymmetric distributions are frequently seen in real-world datasets due to a number of factors, such as sample biases and nonlinear interactions between the variables observed. Thus, in order to better characterize real-world phenomena, studying asymmetric distribution is of great interest. In this work, we derive stress–strength reliability formulas of the type P(X < Y) when both X and Y follow p-max stable laws with three parameters, which are inherently asymmetric. The new relations are given in terms of extreme-value H-functions and have been obtained under fewer parameter restrictions when compared to similar results in the literature. We estimate the parameters of the p-max stable laws by a stochastic optimization method and the stress–strength probability by a maximum likelihood procedure. The performance of the analytical models is evaluated through simulations and real-life dataset modeling.