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Non-Bayesian and Bayesian estimations for Weibull distribution based on progressively type II censored data with binomial removals. (English) Zbl 1220.62121

Summary: This paper deals with the problem of uniformly minimum variance unbiased estimation for a two parameter Weibull distribution based on progressively Type II censored data with binomial removals. We obtain the UMVUE for powers of the scale parameter and its functions, for known shape parameters. The UMVUE of the variance of these estimators are also given. The UMVUE of the density and reliability function at a specified point are derived. Bayes estimators of parameters, reliability function and hazard function are obtained under (i) squared error loss function, (ii) LINEX loss function, and (iii) general entropy loss function. These Bayes estimators are obtained based on conjugate prior for Weibull distribution and binomial distribution. The associated Bayes risks for the parameters are also obtained.

MSC:

62N02 Estimation in survival analysis and censored data
62N01 Censored data models
62F15 Bayesian inference
62N05 Reliability and life testing
62F10 Point estimation
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