Double-Stage Shrinkage Estimation of Reliability Function for Burr XII Distribution

Abstract

This study is concerned with the problem of estimating the reliability function of the parameters of the two-parameter Burr XII distribution when the data are complete. Concepts such as the likelihood estimator, bias, bias ratio, and mean square error are defined. The purpose of this research is investigate the properties of the double-stage shrinkage estimators (DSSEs) of the reliability function of Burr XII distribution and obtain the equations of bias, mean square error, and bias ratio. The relative efficiency of the Burr XII distribution of the proposed estimators is also investigated by deriving their equations. Numerical results show performance of our estimators to be better than those of the classical pooled estimators based on the relative efficiency criteria. In particular, our proposed DSSEs have better performance than the classical estimator and single-stage shrinkage estimators.

Keywords

• Burr XII distribution
• , Shrinkage Estimator
• Reliability function
• Bias
• Mean Squared Error
• Bias Ratio