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On generalized progressive hybrid censoring in presence of competing risks. (English) Zbl 1366.62189
Summary: 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
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[1] Balakrishnan N, Cramer E (2014) The art of progressive censoring. Birkhäuser, New York · Zbl 1365.62001
[2] Balakrishnan, N; Childs, A; Chandrasekar, B, An efficient computational method for moments of order statistics under progressive censoring, Stat Probab Lett, 60, 359-365, (2002) · Zbl 1045.62042
[3] Balakrishnan, N; Xie, Q; Kundu, D, Exact inference for a simple step stress model from the exponential distribution under time constraint, Ann Inst Stat Math, 61, 251-274, (2009) · Zbl 1294.62233
[4] Balakrishnan N, Kundu D (2013) Hybrid censoring models, inferential results and applications. Comput Stat Data Anal 57:166-209 (with discussion) · Zbl 1365.62364
[5] Balakrishnan, N; Cramer, E; Iliopoulos, G, On the method of pivoting the CDF for exact confidence intervals with illustration for exponential Mean under life-test with time constraint, Stat Probab Letters, 89, 124-130, (2014) · Zbl 1288.62046
[6] Bhattacharya, S; Pradhan, B; Kundu, D, Analysis of hybrid censored competing risks data, Statistics, 48, 1138-1154, (2014) · Zbl 1367.62278
[7] Chan, P; Ng, H; Su, F, Exact likelihood inference for the two-parameter exponential distribution under type-II progressively hybrid censoring, Metrika, 78, 747-770, (2015) · Zbl 1333.62230
[8] Chen, SM; Bhattayacharya, GK, Exact confidence bound for an exponential parameter under hybrid censoring, Commun Stat Theory Methodol, 16, 2429-2442, (1987) · Zbl 0628.62097
[9] Childs, A; Chandrasekhar, B; Balakrishnan, N; Kundu, D, Exact likelihood inference based on type-I and type-II hybrid censored samples from the exponential distribution, Ann Inst Stat Math, 55, 319-330, (2003) · Zbl 1049.62021
[10] Cho, Y; Sun, H; Lee, K, Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme, Stat Methodol, 23, 18-34, (2015) · Zbl 07035600
[11] Cohen, AC, Progressively censored samples in life testing, Technometrics, 5, 327-329, (1963) · Zbl 0124.35401
[12] Cox, DR, The analysis of exponentially lifetime distributed lifetime with two types of failures, J R Stat Soc Ser B, 21, 411-421, (1959) · Zbl 0093.15704
[13] Cramer, E; Balakrishnan, N, On some exact distributional results based on type-I progressively hybrid censored data from exponential distribution, Stat Methodol, 10, 128-150, (2013) · Zbl 1365.62061
[14] Crowder M (2001) Classical competing risks. Chapman & Hall/CRC, London · Zbl 0979.62078
[15] Epstein, B, Truncated life tests in the exponential case, Ann Math Stat, 25, 555-564, (1954) · Zbl 0058.35104
[16] Gorny, J; Cramer, E, Exact likelihood inference for exponential distribution under generalized progressive hybrid censoring schemes, Stat Methodol, 29, 70-94, (2016) · Zbl 07035799
[17] Hemmati, F; Khorram, E, Statistical analysis of log-normal distribution under type-II progressive hybrid censoring schemes, Commun Stat Simul Comput, 42, 52-75, (2013) · Zbl 1327.62487
[18] Hoel, DG, A representation of mortality data by competing risks, Biometrics, 28, 475-488, (1972)
[19] Kalbfleish JD, Prentice RL (1980) The statistical analysis of the failure time data. Wiley, New York
[20] Kundu, D; Basu, S, Analysis of incomplete data in presence of competing risks, J Stat Plan Inference, 87, 221-239, (2000) · Zbl 1053.62110
[21] Kundu, D; Joarder, A, Analysis of type-II progressively hybrid censored data, Comput Stat Data Anal, 50, 2509-2528, (2006) · Zbl 1284.62605
[22] Kundu, D; Gupta, RD, Analysis of hybrid life-tests in presence of competing risks, Metrika, 65, 159-170, (2007) · Zbl 1106.62111
[23] Lawless JF (1982) Statistical models and methods for lifetimes data. Wiley, New York · Zbl 0541.62081
[24] Pena, EA; Gupta, AK, Bayes estimation for the Marshall-Olkin exponential distribution, J R Stat Soc Ser B, 52, 379-389, (1990) · Zbl 0697.62025
[25] Prentice, RL; Kalbfleish, JD; Peterson, AV; Flurnoy, N; Farewell, VT; Breslow, NE, The analysis of failure time points in presence of competing risks, Biometrics, 34, 541-554, (1978) · Zbl 0392.62088
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