Calculating Gini Coefficient - Unbiased Estimator

[Jrb599]

Hi I was looking at how to calculate the GINI coefficient and saw two different statements from two websites.

Statement 1:
It has been shown that the sample Gini coefficients defined above need to be multiplied by in order to become unbiased estimators for the population coefficients -http://mathworld.wolfram.com/GiniCoefficient.html

Statement 2:
There does not exist a sample statistic that is in general an unbiased estimator of the population Gini coefficient, like the relative mean difference.-http://en.wikipedia.org/wiki/Gini_coefficient


My assumption is because wolfram is using Mu and not X-bar. Any thoughts/help?

 

[Stephen Tashi]

That's an interesting conflict. Perhaps the $\mu$ mentioned on the Wolfram page is the population mean instead of the sample mean.

 

[Jrb599]

that's what I thought; however, the relative mean difference doesn't have a mu in it, and it doesn't have a unbiased estimator either