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Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring

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  • Manoj Kumar Rastogi
  • Yogesh Mani Tripathi
  • Shuo-Jye Wu

Abstract

We consider the problem of estimating unknown parameters, reliability function and hazard function of a two parameter bathtub-shaped distribution on the basis of progressive type-II censored sample. The maximum likelihood estimators and Bayes estimators are derived for two unknown parameters, reliability function and hazard function. The Bayes estimators are obtained against squared error, LINEX and entropy loss functions. Also, using the Lindley approximation method we have obtained approximate Bayes estimators against these loss functions. Some numerical comparisons are made among various proposed estimators in terms of their mean square error values and some specific recommendations are given. Finally, two data sets are analyzed to illustrate the proposed methods.

Suggested Citation

  • Manoj Kumar Rastogi & Yogesh Mani Tripathi & Shuo-Jye Wu, 2012. "Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2389-2411, July.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:11:p:2389-2411
    DOI: 10.1080/02664763.2012.710899
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    References listed on IDEAS

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    1. William J. Reed, 2011. "A flexible parametric survival model which allows a bathtub-shaped hazard rate function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1665-1680, August.
    2. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    3. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
    4. H. Jiang & M. Xie & L. C. Tang, 2010. "On MLEs of the parameters of a modified Weibull distribution for progressively type-2 censored samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(4), pages 617-627.
    5. Shuo-Jye Wu, 2008. "Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1139-1150.
    6. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
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    Cited by:

    1. Kundan Singh & Amulya Kumar Mahto & Yogesh Mani Tripathi, 2024. "On partially observed competing risks model for Chen distribution under generalized progressive hybrid censoring," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(1), pages 105-135, February.
    2. Manoj Chacko & Rakhi Mohan, 2019. "Bayesian analysis of Weibull distribution based on progressive type-II censored competing risks data with binomial removals," Computational Statistics, Springer, vol. 34(1), pages 233-252, March.
    3. Kyeongjun Lee & Youngseuk Cho, 2017. "Bayesian and maximum likelihood estimations of the inverted exponentiated half logistic distribution under progressive Type II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 811-832, April.
    4. Essam A. Ahmed, 2014. "Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 752-768, April.
    5. Siyi Chen & Wenhao Gui, 2020. "Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(5), pages 1-21, April.
    6. Mohammad Z. Raqab & Omar M. Bdair & Fahad M. Al-Aboud, 2018. "Inference for the two-parameter bathtub-shaped distribution based on record data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 229-253, April.
    7. Manoj Kumar Rastogi & Yogesh Mani Tripathi, 2014. "Estimation for an inverted exponentiated Rayleigh distribution under type II progressive censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2375-2405, November.
    8. Sanku Dey & Tanujit Dey, 2014. "On progressively censored generalized inverted exponential distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2557-2576, December.
    9. Ahmed Elshahhat & Mazen Nassar, 2021. "Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data," Computational Statistics, Springer, vol. 36(3), pages 1965-1990, September.

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