Maximum Likelihood Estimation in the Inverse Weibull Distribution with Type II Censored Data

Abstract

We consider maximum likelihood estimation for the parameters and certain functions of the parameters in the Inverse Weibull (IW) distribution based on type II censored data. The functions under consideration are the Mean Residual Life (MRL), which is very important in reliability studies, and Tail Value at Risk (TVaR), which is an important measure of risk in actuarial studies. We investigated the performance of the MLE of the parameters and derived functions under various experimental conditions using simulation techniques. The performance criteria are the bias and the mean squared error of the estimators. Recommendations on the use of the MLE in this model are given. We found that the parameter estimators are almost unbiased, while the MRL and TVaR estimators are asymptotically unbiased. Moreover, the mean squared error of all estimators decreased for larger sample sizes and it increased when the censoring proportion is increased for a fixed sample size. The conclusion is that the maximum likelihood method of estimation works well for the parameters and the derived functions of the parameter like the MRL and TVaR. Two examples on a real data set are presented to illustrate the application of the methods used in this paper. The first one is on survival time of pigs while the other is on fire losses.