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Inference for Weibull distribution based on progressively type-II hybrid censored data. (English) Zbl 1213.62034
Summary: Progressive Type-II hybrid censoring is a mixture of progressive Type-II and hybrid censoring schemes. We discuss the statistical inference on Weibull parameters when the observed data are progressively Type-II hybrid censored. We derive the maximum likelihood estimators (MLEs) and the approximate maximum likelihood estimators (AMLEs) of the Weibull parameters. We then use the asymptotic distributions of the maximum likelihood estimators to construct approximate confidence intervals. Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters are obtained under suitable priors on the unknown parameters and also by using the Gibbs sampling procedure. Monte Carlo simulations are then performed for comparing the confidence intervals based on all those different methods. Finally, one data set is analyzed for illustrative purposes.

MSC:
62F10 Point estimation
62N01 Censored data models
62E20 Asymptotic distribution theory in statistics
62F25 Parametric tolerance and confidence regions
62F15 Bayesian inference
65C05 Monte Carlo methods
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