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 |
Inverse Chen Distribution, Joint Type-II Censoring, Maximum Likelihood Estimation, Bayesian Estimation, Monte Carlo Simulation
| [1] | Agiwal, V. (2021). Bayesian estimation of stress strength reliability from inverse Chen distribution with application on failure time data. Annals of Data Science, https://doi.org/10.1007/s40745-020-00313-w: 1–31. |
| [2] | Al-Matrafi, B. N. and Abd-Elmougod, G. (2017). Statistical inferences with jointly type-II censored samples from two rayleigh distributions. Global Journal of Pure and Applied Mathematics, 13 (12): 8361–8372. |
| [3] | Asar, Y. and Arabi Belaghi, R. (2020). Inference for two Lomax populations under joint type-II censoring. Communications in Statistics-Simulation and Computation, 10.1080/03610918.2020.1814814: 1–18. |
| [4] | Ashour, S. K. and Abo-Kasem, O. E. (2014). Bayesian and non-Bayesian estimation for two generalized exponential populations under joint type-II censored scheme. Pakistan Journal of Statistics and Operation Research, 10 (1): 57–72. |
| [5] | Balakrishnan, N. and Rasouli, A. (2008). Exact likelihood inference for two exponential populations under joint type-II censoring. Computational Statistics & Data Analysis, 52 (5): 2725–2738. |
| [6] | Chaturvedi, A., Kumar, N., and Kumar, K. (2018). Statistical inference for the reliability functions of a family of lifetime distributions based on progressive Type II right censoring. Statistica, 78 (1): 81–101. |
| [7] | Chaturvedi, A. and Vyas, S. (2017). Estimation and testing procedures for the reliability functions of three parameter Burr distribution under censorings. Statistica, 77 (3): 207–235. |
| [8] | Chen, M.-H. and Shao, Q.-M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8 (1): 69–92. |
| [9] | Dhamecha, H. P. and Patel, M. N. (2021). Estimation of parameters of Kumaraswamy distribution under Type II hybrid censoring. International Journal of Agricultural and Statistical Sciences, 17 (2): 471–478. |
| [10] | Garg, R., Dube, M., and Krishna, H. (2020). Estimation of parameters and reliability characteristics in Lindley distribution using randomly censored data. Statistics, Optimization & Information Computing, 8 (1): 80–97. |
| [11] | Garg, R. and Kumar, K. (2021). On estimation of P (Y < X) for generalized inverted exponential distribution based on hybrid censored data. Statistica, 81 (3): 335–361. |
| [12] | Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). Bayesian Data Analysis. 3rd Ed. CRC press, New York. |
| [13] | Goel, R. and Krishna, H. (2021). Likelihood and Bayesian inference for k Lindley populations under joint type-II censoring scheme. Communications in Statistics-Simulation and Computation, DOI: 10.1080/03610918.2021.1937648: 1–16. |
| [14] | Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57 (1): 97–109. |
| [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. |
| [19] | Kumar, I., and Kumar, K. (2022). On estimation of P (V < U) for inverse Pareto distribution under progressively censored data. International Journal of System Assurance Engineering and Management, 13 (1), 189-202. |
| [20] | Kumar, K. and Garg, R. (2014). Estimation of the parameters of randomly censored generalized inverted Rayleigh distribution. International Journal of Agricultural and Statistical Sciences, 10 (1): 147–155. |
| [21] | Metropolis, N. and Ulam, S. (1949). The Monte Carlo method. Journal of the American statistical association, 44 (247): 335–341. |
| [22] | Srivastava, P. K. and Srivastava, R. (2014). Two parameter inverse Chen distribution as survival model. International Journal of Statistika and Mathematika, 11 (1): 12–16. |
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
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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Download@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}
}
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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