Bayesian Estimation for the Doubly Censored Topp Leone Distribution using Approximate Methods and Fuzzy Type of Priors
The Topp Leone distribution (TLD) is a lifetime model having finite support and U-shaped hazard rate; these features distinguish it from the famous lifetime models such as gamma, Weibull, or Log-normal distribution. The Bayesian methods are very much linked to the Fuzzy sets. The Fuzzy priors can be...
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Published in | Journal of function spaces Vol. 2022; pp. 1 - 15 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
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Hindawi
01.01.2022
Hindawi Limited Wiley |
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Abstract | The Topp Leone distribution (TLD) is a lifetime model having finite support and U-shaped hazard rate; these features distinguish it from the famous lifetime models such as gamma, Weibull, or Log-normal distribution. The Bayesian methods are very much linked to the Fuzzy sets. The Fuzzy priors can be used as prior information in the Bayesian models. This paper considers the posterior analysis of TLD, when the samples are doubly censored. The independent informative priors (IPs) which are very close to the Fuzzy priors have been proposed for the analysis. The symmetric and asymmetric loss functions have also been assumed for the analysis. As the marginal PDs are not available in a closed form, therefore, we have used a Quadrature method (QM), Lindley’s approximation (LA), Tierney and Kadane’s approximation (TKA), and Gibbs sampler (GS) for the approximate estimation of the parameters. A simulation study has been conducted to assess and compare the performance of various posterior estimators. In addition, a real dataset has been analyzed for the illustration of the applicability of the results obtained in the study. The study suggests that the TKA performs better than its counterparts. |
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AbstractList | The Topp Leone distribution (TLD) is a lifetime model having finite support and U-shaped hazard rate; these features distinguish it from the famous lifetime models such as gamma, Weibull, or Log-normal distribution. The Bayesian methods are very much linked to the Fuzzy sets. The Fuzzy priors can be used as prior information in the Bayesian models. This paper considers the posterior analysis of TLD, when the samples are doubly censored. The independent informative priors (IPs) which are very close to the Fuzzy priors have been proposed for the analysis. The symmetric and asymmetric loss functions have also been assumed for the analysis. As the marginal PDs are not available in a closed form, therefore, we have used a Quadrature method (QM), Lindley’s approximation (LA), Tierney and Kadane’s approximation (TKA), and Gibbs sampler (GS) for the approximate estimation of the parameters. A simulation study has been conducted to assess and compare the performance of various posterior estimators. In addition, a real dataset has been analyzed for the illustration of the applicability of the results obtained in the study. The study suggests that the TKA performs better than its counterparts. |
Author | Feroze, Navid Ali, Shajib Noor-ul-Amin, Muhammad Al-Alwan, Ali Alshenawy, R. |
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Cites_doi | 10.1080/00949655.2011.607821 10.1016/j.spl.2014.08.014 10.1080/03610918.2016.1146762 10.1016/S0167-7152(00)00021-3 10.1016/j.csda.2010.01.003 10.1007/BF02888353 10.4064/am42-2-8 10.4197/Sci.24-1.6 10.1080/03610926.2015.1053935 10.1109/TSMCB.2011.2114879 10.1007/s13160-016-0222-z 10.1080/0266476022000030084 10.1016/j.csda.2005.05.002 10.1080/01621459.1955.10501259 10.1007/s00362-010-0320-y 10.9734/BJMCS/2017/33053 10.1371/journal.pone.0195394 10.1109/24.536992 |
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Copyright | Copyright © 2022 Navid Feroze et al. Copyright © 2022 Navid Feroze et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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References | H. A. Bayoud (8) 2016; 14 22 A. Legendre (18) 1805 24 N. Feroze (13) 2013; 7 J. F. Lawless (25) 1982 10 11 12 14 15 H. Linhart (26) 1986 16 17 19 1 2 3 4 5 6 7 9 20 B. N. Pandey (23) 2012 21 |
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SubjectTerms | Approximation Bayesian analysis Fuzzy sets Mathematical models Maximum likelihood method Normal distribution Quadratures |
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Title | Bayesian Estimation for the Doubly Censored Topp Leone Distribution using Approximate Methods and Fuzzy Type of Priors |
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