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Different methods of estimation in two parameter Geometric distribution with randomly censored data

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  • Neha Goel

    (Ch. Charan Singh University)

  • Hare Krishna

    (Ch. Charan Singh University)

Abstract

Random censoring scheme has been extensively discussed in literature for several statistical distribution models. Most of these studies focus on continuous variables with range 0 to ∞. In this paper the lifetime and censoring time variables are assumed to be discrete and a minimum threshold is assumed as a location parameter for failure and censoring times. Here, we study a two parameter geometric distribution with location parameter µ and probability parameter θ using randomly censored data. The importance of the minimum time location parameter is highlighted over the no location parameter case with an example. Some classical estimation methods such as methods of moments, least squares, L-moments and maximum likelihood estimation (MLE) are discussed. Asymptotic confidence intervals for parameters are derived using MLEs. Expected time on test is obtained for the parameters. Bayes estimators are developed under generalized entropy loss function (GELF) assuming informative as well as non-informative priors of the parameters. Maximum likelihood and Bayes estimates under GELF are also developed for the reliability characteristics. Various estimation procedures are compared using a Monte Carlo simulation study. The effect and importance of the minimum threshold parameter is illustrated with a numerical data example.

Suggested Citation

  • Neha Goel & Hare Krishna, 2022. "Different methods of estimation in two parameter Geometric distribution with randomly censored data," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(4), pages 1652-1665, August.
    • Handle: RePEc:spr:ijsaem:v:13:y:2022:i:4:d:10.1007_s13198-021-01520-1
    DOI: 10.1007/s13198-021-01520-1
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    References listed on IDEAS

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    1. Sarhan, Ammar M. & Kundu, Debasis, 2008. "Bayes estimators for reliability measures in geometric distribution model using masked system life test data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1821-1836, January.
    2. Hare Krishna & Neha Goel, 2017. "Maximum Likelihood and Bayes Estimation in Randomly Censored Geometric Distribution," Journal of Probability and Statistics, Hindawi, vol. 2017, pages 1-12, February.
    3. Muhammad Danish & Muhammad Aslam, 2013. "Bayesian estimation for randomly censored generalized exponential distribution under asymmetric loss functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(5), pages 1106-1119.
    4. M. E. Ghitany & S. Al-Awadhi, 2002. "Maximum likelihood estimation of Burr XII distribution parameters under random censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(7), pages 955-965.
    5. H. Krishna & N. Goel, 2018. "Classical and Bayesian inference in two parameter exponential distribution with randomly censored data," Computational Statistics, Springer, vol. 33(1), pages 249-275, March.
    6. Kapil Kumar & Indrajeet Kumar, 2019. "Estimation in Inverse Weibull Distribution Based on Randomly Censored Data," Statistica, Department of Statistics, University of Bologna, vol. 79(1), pages 47-74.
    Full references (including those not matched with items on IDEAS)

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