Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study

• We consider progressively type-II censored data from the Inverse Weibull distribution (IW).
• We derive MLEs, approximate MLEs, LS and Bayes estimate methods of scale and shape parameters of the IW.
• Bayes estimator of shape parameter cannot be expressed in closed forms.
• We suggest using Lindley׳s approximation.
• We conclude that the Bayes estimates outperform the classical methods.

In this article we consider statistical inferences about the unknown parameters of the Inverse Weibull distribution based on progressively type-II censoring using classical and Bayesian procedures. For classical procedures we propose using the maximum likelihood; the least squares methods and the approximate maximum likelihood estimators. The Bayes estimators are obtained based on both the symmetric and asymmetric (Linex, General Entropy and Precautionary) loss functions. There are no explicit forms for the Bayes estimators, therefore, we propose Lindley׳s approximation method to compute the Bayes estimators. A comparison between these estimators is provided by using extensive simulation and three criteria, namely, Bias, mean squared error and Pitman nearness (PN) probability. It is concluded that the approximate Bayes estimators outperform the classical estimators most of the time. Real life data example is provided to illustrate our proposed estimators.