Efficient Estimation of the Burr XII Distribution in Presence of Progressive Censored Samples with Binomial Random Removal

A progressive type II (PTII) censoring schemes has a widely application in lifetime and reliability studies. This work investigates the optimal estimator of the probability density and the cumulative distribution functions of the Burr type XII distribution based on PTII censoring samples. The uniformly minimum variance unbiased, maximum likelihood, maximum product spacing, least squares, and weighted least squares estimators are obtained. The closed form expressions for maximum likelihood and uniform minimum variance unbiased estimator, associated mean squared errors and th tau moment are derived. A simulation study is used to demonstrate theoretical achievements. The outcomes of simulation study showed that the maximum product spacing estimates are preferred over all the other estimates. We examine one real data set to demonstrate the applicability and relevance of the proposed estimators. The results of a real-life analysis reveal that proposed estimators outperform some other competitive models.