Preliminary test estimators of the reliability characteristics for the three parameters Burr XII distribution based on records

Some improved estimators and confidence interval of the parametric functions are proposed based on records from three parameters Burr XII distribution. We propose preliminary test estimators (PTES) of the powers of the parameter and reliability functions based on uniformly minimum variance unbiased estimator, maximum likelihood estimator, best invariant estimator and empirical Bayes estimator. We compare the performance of the proposed PTES with the usual estimators by studying their relative efficiencies based on Monte Carlo simulations. We also construct preliminary test confidence interval (PTCI) for the parameter and study its coverage probability and expected length. The results show that the proposed PTES dominate the usual estimators in a wide range of the parametric space. Also it is seen that the proposed PTCI have higher coverage probability while keeping the shorter width in some domain of parametric space. The paper ends up by analysing a real data set.