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

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), 2022. 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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[15] Joshi, S. and Pandit, P. V. (2018). Estimation of stress strength reliability in s-out-of-k system for a two parameter inverse Chen distribution. Journal of Computer and Mathematical Sciences, 9 (12): 1898–1906.
[16] Kishan, R. and Kumar, J. (2019). Bayesian estimation for the Lindley distribution under progressive Type II censoring with binomial removals. International Journal of Agricultural and Statistical Sciences, 15 (1): 361–369.
[17] Krishna, H., Dube, M., and Garg, R. (2019). Estimation of stress strength reliability of inverse Weibull distribution under progressive first failure censoring. Austrian Journal of Statistics, 48 (1): 14–37.
[18] Krishna, H. and Goel, R. (2022). Jointly type-II censored Lindley distributions. Communications in Statistics-Theory and Methods, 51 (1): 135–149.
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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
  • Department of Statistics, Kirori Mal College, Delhi, India

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

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

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