Estimation for the Type-II Extreme Value Distribution Based on Progressive Type-II Censoring

In this paper, we discuss the statistical inference on the unknown parameters and reliability function of type-II extreme value (EVII) distribution when the observed data are progressively type-II censored. By applying EM algorithm, we obtain maximum likelihood estimates (MLEs). We also suggest approximate maximum likelihood estimators (AMLEs), which have explicit expressions. We provide Bayes estimates using both the symmetric and asymmetric loss functions via squared error loss, LINEX loss, and general entropy loss functions. Bayes estimates are obtained using the idea of Lindley and Markov chain Monte Carlo techniques. Finally, Monte Carlo simulations are presented to illustrate the methods discussed in this paper. Analysis is also carried out for a real data set.