Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme

Ibrahim Elbatal, Naif Alotaibi, Salem A. Alyami, Mohammed Elgarhy and Ahmed R. El-Saeed
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Ibrahim Elbatal: Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
Naif Alotaibi: Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
Salem A. Alyami: Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
Mohammed Elgarhy: The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, Egypt
Ahmed R. El-Saeed: Department of Basic Sciences, Obour High Institute for Management & Informatics, Obour 11848, Egypt

Mathematics, 2022, vol. 10, issue 5, 1-16

Abstract: This work will address the problem of estimating the parameters for the Nadaraj ah–Haghighi (NH) distribution using progressive Type-1 censoring (PT1C) utilizing Bayesian and non-Bayesian approaches. To apply PT1C, censoring times for each stage of censoring needed to be known before the experiment started. To solve this issue of censoring time selection, qauntiles from the NH lifetime distribution will be used as PT1C censoring time points. Maximum likelihood (ML) estimators (MLEs) and asymptotic confidence intervals (ACoIs) are produced with a focus on the censoring technique. Bayes estimates (BEs) and accompanying maximum posterior density (PD) credible interval estimations are also created via the squared error (SEr) loss function. The BEs are evaluated using the Markov Chain Monte Carlo (MCMC) technique and the Metropolis–Hasting (MH) algorithm. An analysis of an actual data set demonstrates the theoretical implications of MLEs and BEs for defined schemes of PT1C samples. Finally, simulation results will be used to compare the performance of the various recommended estimators.

Keywords: progressive Type-1 censoring; Nadaraj ah–Haghighi distribution; Bayesian estimation; Markov Chain Monte Carlo; method of maximum likelihood (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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