A unified flexible Weibull-H family for modeling real-life data with properties, Bayesian and non-Bayesian inference

Afify, Ahmed Z.; Nofal, Zohdy M.; Abdelaziz, Mohamed A.

doi:10.47974/JSMS-1440

Open Access Research Article

A unified flexible Weibull-H family for modeling real-life data with properties, Bayesian and non-Bayesian inference

^*Ahmed Z. AfifyCorresponding authorahmed.afify@fcom.bu.edu.egDepartment of Statistics, Mathematics, and Insurance Benha UniversityBenha, 13511, EgyptView full profile → , Zohdy M. Nofaldr.zohdynofal@fcom.bu.edu.egDepartment of Statistics, Mathematics, and Insurance Benha UniversityBenha, 13511, EgyptView full profile → , Mohamed A. Abdelazizmohamed.abdelaziz@fcom.bu.edu.egDepartment of Statistics, Mathematics, and Insurance Benha UniversityBenha, 13511, EgyptView full profile →

* Corresponding author · click or hover a name for details

pp. 1249–1294Vol. 28Issue 7October 2025DOI: 10.47974/JSMS-1440XML

Received:: 18 Sep 2024
Published Online:: 12 May 2025
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1440
Pages:: 1249–1294

Abstract

The Weibull distribution is a cornerstone in reliability analysis. In this study, we propose a new family of distributions derived from the Weibull model, called the new Weibull-H (NW-H) family. This family features sub-models that can represent diverse failure rate patterns, including bathtub, increasing, unimodal, decreasing, J-shaped, and inverted J-shaped shapes. Additionally, these sub-models produce various density shapes, such as left-skewed, unimodal, symmetric, bimodal, right-skewed, and J-shaped. We explore the mathematical properties of the NW-H family and focus on the parameters of a specific sub-model, the NW-exponential (NWEx), employing ten different estimation techniques, both classical and Bayesian. Bayesian estimators are calculated using three distinct loss functions. Through numerical simulations, we compare and rank these estimation methods based on partial and overall performance. Our results demonstrate that the Bayesian approach consistently yields the most effective parameter estimates for the NWEx across various loss functions. Moreover, we apply the NWEx distribution to three real-world datasets from engineering and industry, showcasing its superior fit and flexibility compared to several competing exponential models.

Keywords

Bayesian estimation Data analysis Maximum likelihood Order statistics Simulation Weibull distribution

Subject Classifications

60E0562F1062F15

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