Some Estimation Methods for the Shape Parameter and Reliability Function of Burr Type XII Distribution / Comparison Study

Abstract

Burr type XII distribution plays an important role in reliability modeling, risk analyzing and process capability estimation. The choice of the best estimation method is one of the goals in estimating parameters of the distribution. The main aim of this paper is to obtain and compare the classical "maximum likelihood and uniformly minimum variance unbiased" estimators and the Bayesian estimators of the shape parameter, ???? and reliability function based on a complete sample when the other shape parameter, ? known. The Bayes estimators are obtained under non-informative priors "Jeffrey’s prior, modified and extension of Jeffrey’s prior" as well as under informative gamma prior based on different symmetric and asymmetric loss functions "squared error, quadratic, LINEX, precautionary and entropy". The Monte Carlo experiment was performed under a wide range of cases and sample size. The estimates of the unknown shape parameter were compared by employing the mean square errors and the estimates of reliability function were compared by employing the integrated mean squared error.

Keywords: Burr type XII distribution; Maximum likelihood estimator; Uniformly Minimum Variance Unbiased estimator; Bayes estimators; non-informative Prior; informative Prior; Squared error loss function; quadratic loss function; LINEX loss function; Precautionary loss function; Entropy Loss function; Mean squared error; integrated mean squared error.