The progressive Type-II hybrid censoring scheme introduced by Kundu and Joarder (Computational Statistics and Data Analysis, 2509-2528, 2006, 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, Cho, Sun and Lee (Statistical Methodology, 23, 18-34, 2015) 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., if T * = Z k:m:n , P (T < Z k:m:n < Z m:m:n , D 1 = i) dz 1 . . . dz k .

In this article we consider the analysis of progressively censored competing risks data obtained from a simple step‐stress experiment. It is assumed that there are only two competing causes of failures at each stress level and the lifetime distribution of each one of them is one parameter exponential distribution. Based on the cumulative exposure model assumption, the conditional maximum likelihood estimators (MLEs) of the unknown parameters can be obtained in explicit forms. Confidence intervals of the unknown parameters based on the exact distributions of the conditional MLEs and percentile bootstrap method, are constructed. Further we obtain Bayes estimates and the associated credible intervals based on a very flexible Beta‐gamma prior on the unknown parameters. A simulation experiment has been performed to observe the performances of the different estimators.

Kundu and Gupta [22] provided the analysis of Type-I hybrid censored competing risks data, when the lifetime distribution of the competing causes of failures follow exponential distribution. In this paper we consider the analysis of Type-II hybrid censored competing risks data. It is assumed that latent lifetime distributions of the competing causes of failures follow independent exponential distributions with different scale parameters. It is observed that the maximum likelihood estimators of the unknown parameters do not always exist. We propose the modified estimators of the scale parameters, which coincide with the corresponding maximum likelihood estimators when they exist, and asymptotically they are equivalent. We obtain the exact distribution of the proposed estimators. Using the exact distributions of the proposed estimators, associated confidence intervals are obtained. The asymptotic and bootstrap confidence intervals of the unknown parameters are also provided. Further, Bayesian inference of some unknown parametric functions under a very flexible Beta-Gamma prior is considered. Bayes estimators and associated credible intervals of the unknown parameters are obtained using Monte Carlo method. Extensive Monte Carlo simulations are performed to see the effectiveness of the proposed estimators and one real data set has been analyzed for the illustrative purposes. It is observed that the proposed model and the method work quite well for this data set.

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