The Gini Index, the Lorenz Curve, and the Total Time on Test Transforms.

摘要

This note points out the connection between some well-known indicators used in economics and a central concept in reliability theory. In particular, the Lorenz curve and the Gini index are shown to relate to the total time on test transform and the cumulative total time on test transform, respectively. Thus, the recently proposed tests for exponentiality based on the Gini statistic inherit the properties of the tests for exponentiality based on the cumulative total time on test statistic.