Jamal F, Alqawba M, Altayab Y, Iqbal T, Afify AZ. A unified exponential-H family for modeling real-life data: Properties and inference.
Heliyon 2024;
10:e27661. [PMID:
38509929 PMCID:
PMC10951600 DOI:
10.1016/j.heliyon.2024.e27661]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Revised: 02/28/2024] [Accepted: 03/05/2024] [Indexed: 03/22/2024] Open
Abstract
The exponential distribution is one of the most widely used statistical distribution for reliability issues. In this paper, we introduce a novel family based on the exponential model, called the new exponential-H (NEx-H) family. The sub-models of the NEx-H family are capable of accommodating variable failure rates, as well as unimodal, bimodal, left-skewed, symmetric, right-skewed, and J-shape densities. The mathematical features of the NEx-H family are derived. The parameters of the NEx-Weibull distribution are estimated by using seven estimation methods. Detailed numerical simulations are presented. Based on our study, the maximum likelihood is the best estimation method for estimating the NEx-Weibull parameters. Three real-life data sets are fitted using the NEx-Weibull distribution. The NEx-Weibull model provides better fit as compared to some competing Weibull models.
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