The Bayesian Estimation and Prediction Process Applied to a Mixture of Weibull and Gompertz Distributions Based on Type-I censoring

Authors

M. M. Mohie El-Din, Dept. of Math., Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt
A. Sadek, Dept. of Math., Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt
A. AL-Dugin, Dept. of Math., Faculty of Science, Al-Azhar University, Nasr City, Cairo, EgyptFollow

Document Type

Original Article

Subject Areas

Mathematics and Statistics

Keywords

Bayesian estimation and prediction, Gompertz distribution, Loss function, Mixture model, Type-I censoring, Weibull distribution

Abstract

We examine different methods to estimate the parameters of a lifetime model represented by a mixture of Weibull and Gompertz distributions, based on Type-I censoring. We derive Bayes estimators with a variety of loss functions, including symmetric Squared Error, asymmetric Linear Exponential, and General Entropy, utilizing both informative and noninformative priors. We also go over how to create the model's two-sample Bayesian prediction intervals. To demonstrate these methods, we provide computational results through Monte Carlo simulations and real data.

How to Cite This Article

El-Din, M. M. Mohie; Sadek, A.; and AL-Dugin, A. (2024) "The Bayesian Estimation and Prediction Process Applied to a Mixture of Weibull and Gompertz Distributions Based on Type-I censoring," Al-Azhar Bulletin of Science: Vol. 35: Iss. 3, Article 3.
DOI: https://doi.org/10.58675/2636-3305.1685