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Math Help - Gini Coefficient

  1. #1
    Junior Member
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    Gini Coefficient

    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 n/(n-1) 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?

    Edit: The only reason I'm still iffy on this is because the relative mean difference does not have an unbiased estimator either and it is not divided by Mu.


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  2. #2
    MHF Contributor
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    Re: Gini Coefficient

    Hey Jrb599.

    Did you try taking the expectations of the test statistic (where possible) to see if you get an un-biased estimator with the correction?- (Example E[G_hat] = G for unbiased-ness)
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  3. #3
    Junior Member
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    Re: Gini Coefficient

    No not yet - I was hoping some could shed some light first.
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