The analysis of progressively censored data has received considerable attention in the last few years. In this paper, we consider the joint progressive censoring scheme for two populations. It is assumed that the lifetime distribution of the items from the two populations follows Weibull distribution with the same shape but different scale parameters. Based on the joint progressive censoring scheme, first, we consider the maximum likelihood estimators of the unknown parameters whenever they exist. We provide the Bayesian inferences of the unknown parameters under a fairly general priors on the shape and scale parameters. The Bayes estimators and the associated credible intervals cannot be obtained in closed form, and we propose to use the importance sampling technique to compute the same. Further, we consider the problem when it is known a priori that the expected lifetime of one population is smaller than the other. We provide the order-restricted classical and Bayesian inferences of the unknown parameters. Monte Carlo simulations are performed to observe the performances of the different estimators and the associated confidence and credible intervals. One real data set has been analyzed for illustrative purpose.
Keywords and phrases
Joint progressive censoring scheme Weibull distribution Beta-gamma distribution Log-concave density function Posterior analysis
AMS (2000) subject classification
Primary 62N01, 62N02 Secondary 62F10.
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Devroye L. (1984). A simple algorithm for generating random variables using log-concave density. Computing33, 246–257.CrossRefGoogle Scholar
Doostparast M., Ahmadi M. V. and Ahmadi J. (2013). Bayes estimation based on joint progressive type-II censored data under LINEX loss function. Communications in Statistics - Simulation and Computation42, 1865–1886.MathSciNetzbMATHGoogle Scholar
Gelman, A., Meng, X. L. and Stern, H. (1996) Posterior predictive assessment of model fitness via realized discrepancies, Statistica sinica, 733–760.Google Scholar
Herd G. R. 1956 Estimation of the parameters of a population from a multi-censored sample, Ph.D. Thesis Iowa State College, Ames, Iowa.Google Scholar
Kundu D. (2008). Bayesian inference and life testing plans for the Weibull distribution in presence of progressive censoring. Technometrics50, 144–154.MathSciNetCrossRefGoogle Scholar
Kundu D. and Gupta R. (2006). Estimation of P[Y < X] for Weibull distributions. IEEE Transactions on Reliability55, 270–280.CrossRefGoogle Scholar
Lemon G. H. (1975). Maximum likelihood estimation for the three parameter Weibull distribution based on censored samples. Technometrics17, 247–254.MathSciNetCrossRefGoogle Scholar
Mann N. R. (1971). Best linear invariant estimation for Weibull parameters under progressive censoring. Technometrics13, 521–533.MathSciNetCrossRefGoogle Scholar
Montanari G. C. and Cacciari M. (1988). Progressively-Censored aging tests on XLPE-Insulated cable models. IEEE Transactions on Electrical Insulation23, 365– 372.CrossRefGoogle Scholar
Ng H. K. T., Chan P. S. and Balakrishnan N. (2004). Optimal Progressive Censoring Plans for the Weibull Distribution. Technometrics46, 470–481.MathSciNetCrossRefGoogle Scholar
Ng H. K. T. and Wang Z. (2009). Statistical estimation for the parameters of Weibull distribution based on progressively type-I interval censored sample. Journal of Statistical Computation and Simulation79, 145–159.MathSciNetCrossRefGoogle Scholar
Parsi S. and Bairamov I. (2009). Expected values of the number of failures for two populations under joint type-II progressive censoring. Computational Statistics and Data Analysis53, 3560–3570.MathSciNetCrossRefGoogle Scholar
Pena E. A. and Gupta A. K. (1990). Bayes estimation for the Marshall-Olkin exponential distribution. Journal of the Royal Statistical Society, Ser. B.52, 379–389. vol. 15, 375–383.MathSciNetzbMATHGoogle Scholar
Rasouli A. and Balakrishnan N. (2010). Exact likelihood inference for two exponential populations under joint progressive type-II censoring. Communications in Statistics - Theory and Methods39, 2172–2191.MathSciNetCrossRefGoogle Scholar
Shafay A. R., Balakrishnan N. and Abdel-Aty Y. (2014). Bayesian inference based on a jointly type-II censored sample from two exponential populations. Journal of Statistical Computation and Simulation84, 2427–2440.MathSciNetCrossRefGoogle Scholar
Su F. 2013 Exact likelihood inference for multiple exponential populations under joint censoring, Ph.D. Thesis McMaster University, Hamilton, Ontario.Google Scholar
Viveros R. and Balakrishnan N. (1994). Interval estimation of parameters of life from progressively censored data. Technometrics36, 84–91.MathSciNetCrossRefGoogle Scholar
Wang B. X., Yu K. and Jones M. C. (2010). Inference under progressive type-II right-censored sampling for certain lifetime distributions. Technometrics52, 453–460.MathSciNetCrossRefGoogle Scholar