A New Generalization of the Uniform Distribution: Properties and Applications to Lifetime Data

Isidro Jesús González-Hernández (), Luis Carlos Méndez-González, Rafael Granillo-Macías, José Luis Rodríguez-Muñoz and José Sergio Pacheco-Cedeño
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Isidro Jesús González-Hernández: Department of Industrial Engineering, Universidad Autónoma del Estado de Hidalgo, Ciudad Sahagún 43998, Hidalgo, Mexico
Luis Carlos Méndez-González: Department of Industrial Engineering and Manufacturing, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez 32310, Chihuahua, Mexico
Rafael Granillo-Macías: Department of Industrial Engineering, Universidad Autónoma del Estado de Hidalgo, Ciudad Sahagún 43998, Hidalgo, Mexico
José Luis Rodríguez-Muñoz: Department of Industrial Engineering, Universidad Autónoma del Estado de Hidalgo, Ciudad Sahagún 43998, Hidalgo, Mexico
José Sergio Pacheco-Cedeño: Department of Industrial Engineering, Universidad Autónoma del Estado de Hidalgo, Ciudad Sahagún 43998, Hidalgo, Mexico

Mathematics, 2024, vol. 12, issue 15, 1-26

Abstract: In this paper, we generalize two new statistical distributions, to improve the ability to model failure rates with non-monotonic, monotonic, and mainly bathtub curve behaviors. We call these distributions Generalized Powered Uniform Distribution and MOE-Powered Uniform. The proposed distributions’ approach is based on incorporating a parameter k in the power of the values of the random variables, which is associated with the Probability Density Function and includes an operator called the Powered Mean. Various statistical and mathematical features focused on reliability analysis are presented and discussed, to make the models attractive to reliability engineering or medicine specialists. We employed the Maximum Likelihood Estimator method to estimate the model parameters and we analyzed its performance through a Monte Carlo simulation study. To demonstrate the flexibility of the proposed approach, a comparative analysis was carried out on four case studies with the proposed MOE-Powered Uniform distribution, which can model failure times as a bathtub curve. The results showed that this new model is more flexible and useful for performing reliability analysis.

Keywords: Marshall–Olkin distributions; generalized uniform distribution; maximum likelihood estimation; Monte Carlo simulation; reliability analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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