Estimation of P(X < Y) stress-strength reliability measures for a class of asymmetric distributions : the case of three-parameter p-max stable laws
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| Hlavní autor: | |
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| Datum vydání: | 2024 |
| Další autoři: | , , |
| Médium: | Article |
| Jazyk: | eng |
| Zdroj: | Repositório Institucional da UnB |
| Download full: | 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 |
Shrnutí: | 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. |