Analyzing quantitative performance: Bayesian estimation of 3-component mixture geometric distributions based on Kumaraswamy prior

Nadeem Akhtar (), Sajjad Ahmad Khan (), Emad A. A. Ismail (), Fuad A. Awwad (), Akbar Ali Khan (), Taza Gul () and Haifa Alqahtani ()
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Nadeem Akhtar: Islamia College Peshawar
Sajjad Ahmad Khan: Islamia College Peshawar
Emad A. A. Ismail: King Saud University
Fuad A. Awwad: King Saud University
Akbar Ali Khan: Higher Education Department
Taza Gul: University of Cambridge
Haifa Alqahtani: United Arab Emirates University

Statistical Papers, 2024, vol. 65, issue 7, No 15, 4451 pages

Abstract: Abstract This research addresses the underutilization of discrete life testing models and proposes a Bayesian estimation strategy for a 3-component mixture of geometric distributions under a doubly type-I censoring scheme. Simpler models are less good at capturing how different processes work than more complex ones. This is because simpler models only show the lifetime distributions. This paper focuses on the examination of a 3-component mixture of geometric distributions from a Bayesian perspective. We conduct the analysis within a censored sampling environment, a commonly employed method in reliability theory and survival analysis. We derive expressions for Bayes estimators and Bayes risks under the Squared Error Loss Function (SELF), the Precautionary Loss Function (PLF), and the DeGroot Loss Function (DLF) using the Kumaraswamy prior. The process includes the elicitation of hyperparameters for the Kumaraswamy prior. Notably, the study recommends the use of the SELF for optimal estimation parameters of the 3-component mixture of geometric distributions under the doubly type-I censoring scheme. This exploration contributes to advancing the application of the Bayesian approach in discrete life testing, providing valuable insights for researchers and practitioners in the field. To numerically assess the performance of Bayes estimators employing Kumaraswamy prior under different loss functions, we conducted simulations to investigate their statistical properties. This analysis involved different sample sizes and test termination times. Furthermore, to underscore the practical relevance of our findings, we present an illustrative example based on real-life data.

Keywords: Bayesian estimations; Geometric distribution; Bayes risks; Bayes estimates censored data; Kumaraswamy prior (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01562-0

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