Título:	Estimation of P(X < Y) for Fréchet, reversed Weibull and Weibull distributions : analytical expressions, simulations and applications
Autor(es):	Fonseca, Tiago Alves da Quintino, Felipe Sousa Ozelim, Luan Carlos de Sena Monteiro Rathie, Pushpa Narayan
Afiliação do autor:	University of Brasília, Gama Engineering College University of Brasília, Department of Statistics University of Brasília, Department of Civil and Environmental Engineering University of Brasília, Department of Statistics
Assunto:	Distribuição (Probabilidades) Teoria dos valores extremos Confiabilidade stress-strength Simulação de Monte Carlo Distribuição de Fréchet Distribuição de Weibull Modelagem estatística
Data de publicação:	2024
Editora:	American Institute of Mathematical Sciences (AIMS)
Referência:	FONSECA, Tiago A. da et al. Estimation of P(X < Y) for Fréchet, reversed Weibull and Weibull distributions: analytical expressions, simulations and applications. Networks and Heterogeneous Media, v. 19, n. 4, p. 1424-1447, 2024. DOI: https://doi.org/10.3934/nhm.2024061. Disponível em: https://doi.org/10.3934/nhm.2024061
Abstract:	This work aimed to derive new analytical formulas for the stress–strength reliability of the type $ P(X < Y) $ when both $ X $ and $ Y $ follow Fréchet, reversed Weibull or Weibull distributions. The new expressions were given in terms of extreme value $ \mathbb{H} $-functions and have been obtained under fewer parameter restrictions while compared to similar results in the literature of these distributions. The performance of the maximum likelihood estimator was evaluated through Monte-Carlo simulations and the results were compared with a nonparametric estimator. Three real dataset applications were carried out. First, we analyzed the statistical behavior of financial assets' returns, showing how $ P(X < Y) $ can be used to build an interesting approach to perform asset selection. Second, minimum monthly flows of water were analyzed. Finally, we compared failure voltage levels of two types of electrical cable insulation. For all the real case applications, confidence intervals for $ P(X < Y) $ were obtained by Bootstrap methods.
Unidade Acadêmica:	Faculdade de Ciências e Tecnologias em Engenharia (FCTE) – Campus UnB Gama Instituto de Ciências Exatas (IE) Departamento de Estatística (IE EST) Faculdade de Tecnologia (FT) Departamento de Engenharia Civil e Ambiental (FT ENC)
Licença:	This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)
DOI:	https://doi.org/10.3934/nhm.2024061
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