A New Approach for the Identification of a Regression Locus for Estimating CDF-Failure Equations on Rectified Plots

Abstract

In estimating the cumulative density function of data, investigators selectively transform the data and their order statistics in order to achieve rectification of the data string. Ordinary least-squares regression procedures no longer apply because of the transformations. Investigators are often seeking a fifty-percent (median) locus, which least-squares methods do not ordinarily discover. A weighted least-squares regression procedure is presented that will establish an estimate of the mean CDF line and through appropriate rotation, provide an estimate of the median CDF line. Examples from common distributions follow a general development.