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- Title
A New Generalization of the Uniform Distribution: Properties and Applications to Lifetime Data.
- Authors
González-Hernández, Isidro Jesús; Méndez-González, Luis Carlos; Granillo-Macías, Rafael; Rodríguez-Muñoz, José Luis; Pacheco-Cedeño, José Sergio
- 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.
- Subjects
PROBABILITY density function; MAXIMUM likelihood statistics; RELIABILITY in engineering; RANDOM variables; DISTRIBUTION (Probability theory)
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 15, p2328
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12152328