Estimation of P(X < Y) stress-strength reliability measures for a class of asymmetric distributions : the case of three-parameter p-max stable laws

• Autor(a) principal: Quintino, Felipe Sousa
• Data de Publicação: 2024
• Outros Autores: Rathie, Pushpa Narayan, Ozelim, Luan Carlos de Sena Monteiro, Fonseca, Tiago Alves da
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UnB
• Texto Completo: http://repositorio.unb.br/handle/10482/50621; https:/doi.org/10.3390/sym16070837; https://orcid.org/0000-0003-0286-0541; https://orcid.org/0000-0002-9790-369X; https://orcid.org/0000-0002-2581-0486; https://orcid.org/0009-0004-5147-4393
• topic: Confiabilidade tensão-resistência; Distribuições assimétricas; Probabilidades

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.