On generalized progressive hybrid censoring in presence of competing risks.

*(English)*Zbl 1366.62189Summary: The progressive Type-II hybrid censoring scheme introduced by D. Kundu and A. Joarder [Comput. Stat. Data Anal. 50, No. 10, 2509–2528 (2006; Zbl 1284.62605)], has received some attention in the last few years. One major drawback of this censoring scheme is that very few observations (even no observation at all) may be observed at the end of the experiment. To overcome this problem, Y. Cho et. al. [“Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme”, Stat. Methodol. 23, 18–34 (2015; doi:10.1016/j.stamet.2014.09.002)] (see also [K. Lee et al., J. Korean Stat. Soc. 45, No. 1, 123–136 (2016; Zbl 1330.62363)]) recently introduced generalized progressive censoring which ensures to get a pre specified number of failures. In this paper we analyze generalized progressive censored data in presence of competing risks. For brevity we have considered only two competing causes of failures, and it is assumed that the lifetime of the competing causes follow one parameter exponential distributions with different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters and also provide their exact distributions. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals can be obtained. Asymptotic and bootstrap confidence intervals are also provided for comparison purposes. We further consider the Bayesian analysis of the unknown parameters under a very flexible beta-gamma prior. We provide the Bayes estimates and the associated credible intervals of the unknown parameters based on the above priors. We present extensive simulation results to see the effectiveness of the proposed method and finally one real data set is analyzed for illustrative purpose.

##### MSC:

62N05 | Reliability and life testing |

62F10 | Point estimation |

62F15 | Bayesian inference |

62F25 | Parametric tolerance and confidence regions |

62N01 | Censored data models |

##### Keywords:

competing risk; generalized progressive hybrid censoring; beta-gamma distribution; maximum likelihood estimator; bootstrap confidence interval; Bayes credible interval
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\textit{A. Koley} and \textit{D. Kundu}, Metrika 80, No. 4, 401--426 (2017; Zbl 1366.62189)

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