Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring

Shrawan Kumar; Anita Kumari; Kapil Kumar

doi:doi:10.11648/j.ajtas.20221105.12

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Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring

Shrawan Kumar, Anita Kumari, Kapil Kumar

Published in American Journal of Theoretical and Applied Statistics (Volume 11, Issue 5)

Received: 1 September 2022 Accepted: 19 September 2022 Published: 28 September 2022

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Abstract

In the era of growing technologies and demand for more reliable products, comparative studies of products from different lines of manufacturing units have become essential. Due to the time-saving and cost-effectiveness properties, the joint Type-II censoring scheme is beneficial for dealing with such types of comparative studies. The inverse Chen distribution has the upside-down or unimodal failure rate function, and it is a suitable lifetime model in life testing and reliability theory. This article contains the Bayesian and classical estimations in the inverse Chen distribution under joint type-II censoring. The maximum likelihood estimators and the corresponding asymptotic confidence intervals of the unknown parameters are developed in the classical estimation approach. In the case of the Bayesian estimation approach, the Bayes estimators of the unknown parameters under the squared error loss function using gamma informative priors are computed. The Bayes estimates are calculated using Markov chain Monte Carlo (MCMC) techniques. Also, the highest posterior density (HPD) credible intervals of the unknown parameters are constructed using MCMC methods. To study various estimates developed in this article, a Monte Carlo simulation study is performed. To compare various estimates, the average estimate, mean squared error values along with the average length and the coverage probabilities are considered. Finally, a real-life problem is analysed to show the applicability of the proposed estimation methods.

Published in	American Journal of Theoretical and Applied Statistics (Volume 11, Issue 5)
DOI	10.11648/j.ajtas.20221105.12
Page(s)	150-159
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Inverse Chen Distribution, Joint Type-II Censoring, Maximum Likelihood Estimation, Bayesian Estimation, Monte Carlo Simulation

References

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APA Style

Shrawan Kumar, Anita Kumari, Kapil Kumar. (2022). Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring. American Journal of Theoretical and Applied Statistics, 11(5), 150-159. https://doi.org/10.11648/j.ajtas.20221105.12

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ACS Style

Shrawan Kumar; Anita Kumari; Kapil Kumar. Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring. Am. J. Theor. Appl. Stat. 2022, 11(5), 150-159. doi: 10.11648/j.ajtas.20221105.12

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AMA Style

Shrawan Kumar, Anita Kumari, Kapil Kumar. Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring. Am J Theor Appl Stat. 2022;11(5):150-159. doi: 10.11648/j.ajtas.20221105.12

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@article{10.11648/j.ajtas.20221105.12,
  author = {Shrawan Kumar and Anita Kumari and Kapil Kumar},
  title = {Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {5},
  pages = {150-159},
  doi = {10.11648/j.ajtas.20221105.12},
  url = {https://doi.org/10.11648/j.ajtas.20221105.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221105.12},
  abstract = {In the era of growing technologies and demand for more reliable products, comparative studies of products from different lines of manufacturing units have become essential. Due to the time-saving and cost-effectiveness properties, the joint Type-II censoring scheme is beneficial for dealing with such types of comparative studies. The inverse Chen distribution has the upside-down or unimodal failure rate function, and it is a suitable lifetime model in life testing and reliability theory. This article contains the Bayesian and classical estimations in the inverse Chen distribution under joint type-II censoring. The maximum likelihood estimators and the corresponding asymptotic confidence intervals of the unknown parameters are developed in the classical estimation approach. In the case of the Bayesian estimation approach, the Bayes estimators of the unknown parameters under the squared error loss function using gamma informative priors are computed. The Bayes estimates are calculated using Markov chain Monte Carlo (MCMC) techniques. Also, the highest posterior density (HPD) credible intervals of the unknown parameters are constructed using MCMC methods. To study various estimates developed in this article, a Monte Carlo simulation study is performed. To compare various estimates, the average estimate, mean squared error values along with the average length and the coverage probabilities are considered. Finally, a real-life problem is analysed to show the applicability of the proposed estimation methods.},
 year = {2022}
}

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TY - JOUR
T1 - Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring
AU - Shrawan Kumar
AU - Anita Kumari
AU - Kapil Kumar
Y1 - 2022/09/28
PY - 2022
N1 - https://doi.org/10.11648/j.ajtas.20221105.12
DO - 10.11648/j.ajtas.20221105.12
T2 - American Journal of Theoretical and Applied Statistics
JF - American Journal of Theoretical and Applied Statistics
JO - American Journal of Theoretical and Applied Statistics
SP - 150
EP - 159
PB - Science Publishing Group
SN - 2326-9006
UR - https://doi.org/10.11648/j.ajtas.20221105.12
AB - In the era of growing technologies and demand for more reliable products, comparative studies of products from different lines of manufacturing units have become essential. Due to the time-saving and cost-effectiveness properties, the joint Type-II censoring scheme is beneficial for dealing with such types of comparative studies. The inverse Chen distribution has the upside-down or unimodal failure rate function, and it is a suitable lifetime model in life testing and reliability theory. This article contains the Bayesian and classical estimations in the inverse Chen distribution under joint type-II censoring. The maximum likelihood estimators and the corresponding asymptotic confidence intervals of the unknown parameters are developed in the classical estimation approach. In the case of the Bayesian estimation approach, the Bayes estimators of the unknown parameters under the squared error loss function using gamma informative priors are computed. The Bayes estimates are calculated using Markov chain Monte Carlo (MCMC) techniques. Also, the highest posterior density (HPD) credible intervals of the unknown parameters are constructed using MCMC methods. To study various estimates developed in this article, a Monte Carlo simulation study is performed. To compare various estimates, the average estimate, mean squared error values along with the average length and the coverage probabilities are considered. Finally, a real-life problem is analysed to show the applicability of the proposed estimation methods.
VL - 11
IS - 5
ER -

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Author Information

Shrawan Kumar

Department of Statistics, Kirori Mal College, Delhi, India
Anita Kumari

Department of Statistics, Central University of Haryana, Mahendergarh, India
Kapil Kumar

Department of Statistics, Central University of Haryana, Mahendergarh, India

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APA Style

Shrawan Kumar, Anita Kumari, Kapil Kumar. (2022). Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring. American Journal of Theoretical and Applied Statistics, 11(5), 150-159. https://doi.org/10.11648/j.ajtas.20221105.12

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ACS Style

Shrawan Kumar; Anita Kumari; Kapil Kumar. Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring. Am. J. Theor. Appl. Stat. 2022, 11(5), 150-159. doi: 10.11648/j.ajtas.20221105.12

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AMA Style

Shrawan Kumar, Anita Kumari, Kapil Kumar. Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring. Am J Theor Appl Stat. 2022;11(5):150-159. doi: 10.11648/j.ajtas.20221105.12

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@article{10.11648/j.ajtas.20221105.12,
  author = {Shrawan Kumar and Anita Kumari and Kapil Kumar},
  title = {Bayesian and Classical Inferences in Two Inverse Chen Populations Based on Joint Type-II Censoring},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {5},
  pages = {150-159},
  doi = {10.11648/j.ajtas.20221105.12},
  url = {https://doi.org/10.11648/j.ajtas.20221105.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221105.12},
  abstract = {In the era of growing technologies and demand for more reliable products, comparative studies of products from different lines of manufacturing units have become essential. Due to the time-saving and cost-effectiveness properties, the joint Type-II censoring scheme is beneficial for dealing with such types of comparative studies. The inverse Chen distribution has the upside-down or unimodal failure rate function, and it is a suitable lifetime model in life testing and reliability theory. This article contains the Bayesian and classical estimations in the inverse Chen distribution under joint type-II censoring. The maximum likelihood estimators and the corresponding asymptotic confidence intervals of the unknown parameters are developed in the classical estimation approach. In the case of the Bayesian estimation approach, the Bayes estimators of the unknown parameters under the squared error loss function using gamma informative priors are computed. The Bayes estimates are calculated using Markov chain Monte Carlo (MCMC) techniques. Also, the highest posterior density (HPD) credible intervals of the unknown parameters are constructed using MCMC methods. To study various estimates developed in this article, a Monte Carlo simulation study is performed. To compare various estimates, the average estimate, mean squared error values along with the average length and the coverage probabilities are considered. Finally, a real-life problem is analysed to show the applicability of the proposed estimation methods.},
 year = {2022}
}

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