Analysis of the generalized progressive hybrid censoring from Burr Type-Ⅻ lifetime model

Magdy Nagy; Khalaf S. Sultan; Mahmoud H. Abu-Moussa; Magdy Nagy; Khalaf S. Sultan; Mahmoud H. Abu-Moussa

doi:10.3934/math.2021564

AIMS Mathematics

2021, Volume 6, Issue 9: 9675-9704. doi: 10.3934/math.2021564

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Research article

Analysis of the generalized progressive hybrid censoring from Burr Type-Ⅻ lifetime model

1.
Department of Statistics and Operation Research, Faculty of Science, King Saud University, KSA
2.
Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt
3.
Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt
4.
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

Received: 12 April 2021 Accepted: 22 June 2021 Published: 28 June 2021
MSC : 62G30, 62F15

In this paper, we use the generalized progressive hybrid censoring sample from the Burr Type-Ⅻ distribution to estimate the unknown parameters, reliability and hazard functions. We apply the maximum likelihood (ML) and the Bayesian estimation under different prior distributions and different loss functions; namely; are the squared error, Linex and general entropy. Also, we construct the classical and credible intervals of the unknown parameters as well as for the survival and hazard functions. In addition, we investigate the performance of the point estimation by using the mean square error (MSE) and expected bias (EB) and performance of the interval estimation using the average length and coverage probability. Further, we develop the Bayesian one- and two- samples Bayesan prediction for the non-observed failures in the progressive censoring. In order to show the performance and usefulness of the inferential procedures, we carry out some simulation experiments using MCMC Algorithm for the Bayesian approach based on different prior distributions. Finally, we apply the theatrical finding to some real life data set.
Citation: Magdy Nagy, Khalaf S. Sultan, Mahmoud H. Abu-Moussa. Analysis of the generalized progressive hybrid censoring from Burr Type-Ⅻ lifetime model[J]. AIMS Mathematics, 2021, 6(9): 9675-9704. doi: 10.3934/math.2021564

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Abstract

In this paper, we use the generalized progressive hybrid censoring sample from the Burr Type-Ⅻ distribution to estimate the unknown parameters, reliability and hazard functions. We apply the maximum likelihood (ML) and the Bayesian estimation under different prior distributions and different loss functions; namely; are the squared error, Linex and general entropy. Also, we construct the classical and credible intervals of the unknown parameters as well as for the survival and hazard functions. In addition, we investigate the performance of the point estimation by using the mean square error (MSE) and expected bias (EB) and performance of the interval estimation using the average length and coverage probability. Further, we develop the Bayesian one- and two- samples Bayesan prediction for the non-observed failures in the progressive censoring. In order to show the performance and usefulness of the inferential procedures, we carry out some simulation experiments using MCMC Algorithm for the Bayesian approach based on different prior distributions. Finally, we apply the theatrical finding to some real life data set.

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