On Estimating the Reliability Function of an Exponential-Pareto II Distribution Using Weighted Least Squares Method

Abstract

The reliability function of the two-parameter Pareto distribution fits income and property value distributions pretty well and explains much of what we see in the real world. For controlled data, the reliability function is usually estimated by the least square method if there is no contamination; if there is contamination, the computation process gets complicated, especially if the model is not linear.

This study suggests the weighted least square estimation to figure out the reliability function's parameters. This method is short and easy to implement. It can be used with the nonlinear model with simulated cases; this study will show that the weighted least square estimator performs better than the ordinary least unbiased estimator.