Journal of Quality Engineering and Management

Bayesian inference of the parameters under the generalized power Lindley distribution based on the hybrid type-II censoring scheme: a simulation study and application

Document Type : Original Article

Authors

Nassrin Baloch Roodbary 1
Iman Makhdoom 2

1 Department of Statistics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.

2 Department of Statistics, Payam Noor University, Tehran, Iran.

https://doi.org/10.48313/jqem.2024.218909
Abstract
Purpose: In this paper, we examine the Bayesian inference of the parameters of the generalized power Lindley distribution in the presence of type two hybrid censored data.
Methodology: To estimate the maximum likelihood of the parameters, given that the estimates cannot be obtained implicitly and do not have a closed-form solution, we employ the EM algorithm and use the Fisher information matrix to construct asymptotic confidence intervals. Additionally, when estimating the parameters of the generalized power Lindley distribution, which we denote EPL throughout the article, we employ two Lindley approximation methods and Markov chain Monte Carlo under the squared-error loss function. We obtain HPD confidence intervals according to Bayesian estimates. Then we compare two Bayesian methods using simulation studies.
Findings: The Monte Carlo method for the three-parameter distribution shows less bias and greater consistency than the Bayesian parameter estimates derived from the Lindley approximation. In high-dimensional distributions, the MCMC method yields more accurate forecasts than the Lindley approximation, and convergence occurs more rapidly. The MSE estimates from the Lindley approximation, as shown in Table 2, are significantly larger than the data dispersion for a similar sample size from the MCMC method, as presented in Table 3. We also provide an example of real data.
Originality/Value: Given that no study has been conducted so far on the generalized Lindley power distribution in the presence of censored hybrid type II, the findings of this study can be used for future studies.

Keywords

Bayesian estimation
Maximum likelihood estimation
Generalized Lindley power
Monte Carlo Markov chain
EM algorithm
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Journal of Quality Engineering and Management
Volume 14, Issue 2
Summer 2024
Pages 177-198

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