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Math Help - Proof or relationship between generalised entropy and Atkinson indexes

  1. #1
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    Proof or relationship between generalised entropy and Atkinson indexes

    Hi, see attached this difficult proof in pdf format.

    This result can be shown to be correct computationally, but is there an analytic solution?

    Any guidance would be most appreciated.

    Edit: see also these additional identities that may be useful.
    Attached Files Attached Files
    Last edited by frustrated; September 27th 2012 at 10:27 PM.
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  2. #2
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    Re: Proof or relationship between generalised entropy and Atkinson indexes

    Hey frustrated.

    Have you looked at the Central Limit Theorem? This theorem is basically what makes a lot of the statistical results work and it's also the basis for a lot of the Weiner Process and Brownian motion stuff in Finance and applied statistics that use this.
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  3. #3
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    Re: Proof or relationship between generalised entropy and Atkinson indexes

    Not really, but I will now in depth.

    Edit: Ok CLT is now familiar, but have not looked at the proofs. We are already implicitly using this as there is an assumption of a smooth log-normal distribution.

    Edit: it should be noted that this problem is scale invariant, so the real value of ybar is irrelevant.
    Last edited by frustrated; September 28th 2012 at 12:08 AM.
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