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Inference for log‐location‐scale family of distributions under competing risks with progressive type‐I interval censored data

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  • Soumya Roy
  • Biswabrata Pradhan

Abstract

In this article, we present statistical inference of unknown lifetime parameters based on a progressive Type‐I interval censored dataset in presence of independent competing risks. A progressive Type‐I interval censoring scheme is a generalization of an interval censoring scheme, allowing intermediate withdrawals of test units at the inspection points. We assume that the lifetime distribution corresponding to a failure mode belongs to a log‐location‐scale family of distributions. Subsequently, we present the maximum likelihood analysis for unknown model parameters. We observe that the numerical computation of the maximum likelihood estimates can be significantly eased by developing an expectation‐maximization algorithm. We demonstrate the same for three popular choices of the log‐location‐scale family of distributions. We then provide Bayesian inference of the unknown lifetime parameters via Gibbs Sampling and a related data augmentation scheme. We compare the performance of the maximum likelihood estimators and Bayesian estimators using a detailed simulation study. We also illustrate the developed methods using a progressive Type‐I interval censored dataset.

Suggested Citation

  • Soumya Roy & Biswabrata Pradhan, 2023. "Inference for log‐location‐scale family of distributions under competing risks with progressive type‐I interval censored data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 208-232, May.
    • Handle: RePEc:bla:stanee:v:77:y:2023:i:2:p:208-232
    DOI: 10.1111/stan.12282
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    References listed on IDEAS

    as
    1. Soumya Roy & Chiranjit Mukhopadhyay, 2014. "Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2429-2451, May.
    2. Fernández, Carmen & Steel, Mark F. J., 1999. "Reference priors for the general location-scale modelm," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 377-384, July.
    3. Budhiraja, Sonal & Pradhan, Biswabrata & Sengupta, Debasis, 2017. "Maximum likelihood estimators under progressive Type-I interval censoring," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 202-209.
    4. J. F. Lawless & Denise Babineau, 2006. "Models for interval censoring and simulation-based inference for lifetime distributions," Biometrika, Biometrika Trust, vol. 93(3), pages 671-686, September.
    5. Chandrakant Lodhi & Yogesh Mani Tripathi, 2020. "Inference on a progressive type I interval-censored truncated normal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(8), pages 1402-1422, June.
    6. Chen, D.G. & Lio, Y.L., 2010. "Parameter estimations for generalized exponential distribution under progressive type-I interval censoring," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1581-1591, June.
    7. Mahdi Alimohammadi & Mohammad Hossein Alamatsaz & Erhard Cramer, 2016. "Convolutions and generalization of logconcavity: Implications and applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 109-123, March.
    8. Arnab Koley & Debasis Kundu, 2021. "Analysis of progressive Type‐II censoring in presence of competing risk data under step stress modeling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 115-136, May.
    9. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    10. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
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