Analysis of progressive Type-Ⅱ censoring schemes for generalized power unit half-logistic geometric distribution

Ahmed R. El-Saeed; Ahmed T. Ramadan; Najwan Alsadat; Hanan Alohali; Ahlam H. Tolba; Ahmed R. El-Saeed; Ahmed T. Ramadan; Najwan Alsadat; Hanan Alohali; Ahlam H. Tolba

doi:10.3934/math.20231577

AIMS Mathematics

2023, Volume 8, Issue 12: 30846-30874. doi: 10.3934/math.20231577

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Analysis of progressive Type-Ⅱ censoring schemes for generalized power unit half-logistic geometric distribution

1.
Department of Basic Sciences, Obour High Institute for Management & Informatics, Egypt
2.
Department of Basic Sciences, High Raya Institute, Damietta 34511, Egypt
3.
Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
4.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
5.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 30 August 2023 Revised: 30 October 2023 Accepted: 05 November 2023 Published: 15 November 2023
MSC : 62F15, 62G20, 65C60

This study addresses the difficulties associated with parameter estimation in the generalized power unit half-logistic geometric distribution by employing a progressive Type-Ⅱ censoring technique. The study uses a variety of methods, including maximum likelihood, maximum product of spacing, and Bayesian estimation. The work investigates Bayesian estimators taking into account a gamma prior and a symmetric loss function while working with observed data produced by likelihood and spacing functions. A full simulation experiment is carried out with varying sample sizes and censoring mechanisms in order to thoroughly evaluate the various estimation approaches. The highest posterior density approach is employed in the study to compute credible intervals for the parameters. Additionally, based on three optimal criteria, the study chooses the best progressive censoring scheme from a variety of rival methods. The study examines two real datasets in order to confirm the applicability of the generalized power unit half-logistic geometric distribution and the efficacy of the suggested estimators. The results show that in order to generate the necessary estimators, the maximum product of the spacing approach is better than the maximum likelihood method. Furthermore, as compared to traditional methods, the Bayesian strategy that makes use of probability and spacing functions produces estimates that are more satisfactory.
Citation: Ahmed R. El-Saeed, Ahmed T. Ramadan, Najwan Alsadat, Hanan Alohali, Ahlam H. Tolba. Analysis of progressive Type-Ⅱ censoring schemes for generalized power unit half-logistic geometric distribution[J]. AIMS Mathematics, 2023, 8(12): 30846-30874. doi: 10.3934/math.20231577

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Abstract

This study addresses the difficulties associated with parameter estimation in the generalized power unit half-logistic geometric distribution by employing a progressive Type-Ⅱ censoring technique. The study uses a variety of methods, including maximum likelihood, maximum product of spacing, and Bayesian estimation. The work investigates Bayesian estimators taking into account a gamma prior and a symmetric loss function while working with observed data produced by likelihood and spacing functions. A full simulation experiment is carried out with varying sample sizes and censoring mechanisms in order to thoroughly evaluate the various estimation approaches. The highest posterior density approach is employed in the study to compute credible intervals for the parameters. Additionally, based on three optimal criteria, the study chooses the best progressive censoring scheme from a variety of rival methods. The study examines two real datasets in order to confirm the applicability of the generalized power unit half-logistic geometric distribution and the efficacy of the suggested estimators. The results show that in order to generate the necessary estimators, the maximum product of the spacing approach is better than the maximum likelihood method. Furthermore, as compared to traditional methods, the Bayesian strategy that makes use of probability and spacing functions produces estimates that are more satisfactory.

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