A Simulation Study on the Bounds of the Gini's Mean Difference for Data with a unit Standard Deviation

摘要

Baker L. has given lower and upper bounds for the ratio of Gini's mean difference to the standard deviation of a data. The purpose of this study is to examine the bounds for the data of different sample sizes, generated from different distributions. A simulation study is performed to study the bounds for variety of discrete and continuous distributions. Under the statistical analysis of the various sets of sample data, it is observed that lower bounds violate the results provided in Baker's paper.