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Re: st: Ancestry nominal dispersion measures like the Herfindahl, was Re: st: loops for regions


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Ancestry nominal dispersion measures like the Herfindahl, was Re: st: loops for regions
Date   Fri, 7 Sep 2012 18:29:55 +0100

Thanks for taking up the challenge.

I was thinking of Gini about 1915, so none of these trump that. I am
away from most of my relevant books, so can't give the precise
reference.

I am not distinguishing for historical purposes between sum of squared
probabilities, its complement, or its reciprocal and regard coming up
with any of these as equally noteworthy.

Nick

On Fri, Sep 7, 2012 at 5:41 PM, Lacy,Michael <Michael.Lacy@colostate.edu> wrote:
> (Given the tangential relevance of the original thread subject to this followup, I thought it better to start a new one.)
>
>
> On 09/05/2012, Nick Cox <njcoxstata@gmail.com> wrote:
>
>>>> This index, although often attributed to Herfindahl by economists who
>>>> know only their only literature, was in essence invented decades
>>>> before by Gini. I don't have the reference in my head, but I think it
>>>> is in Bishop, Y., Fienberg, S.E. and Holland, P.W. 1975. Discrete
>>>> multivariate analysis. Cambridge, MA: MIT Press. Please trump me by
>>>> providing a yet earlier reference.
>>>>
>
> I can't resist the rare opportunity to trump Nick Cox, or at least be invited to try. <grin?
>
>
> One canonical source on this kind of index  is:
>
> Simpson, E.H.  1949 "Measurement of diversity." Nature 163:688.
> who cites the following (his citation style, not mine):
>
> Yule, "Statistical Study of Literary Vocabulary" (Cambridge,1944).
> Fisher, Corbet and Willbarns, J. Animal Ecol., 12, 42 (194s).
> WilIIams, Nature, 157. 482 (1946).
>
> A very thorough source with standing among sociologists is:
>
> Agresti, A. and Finlay, B. 1978.  " Statistical Analysis of Qualitative Variation.  Sociological Methodology, Vol. 9.  Wiley-Blackwell.
> who mentions Gini in passing and more specifically cites (inter alia):
>
> Mueller, J.H. and Schuessler, K. F. 1961.  Statistical Reasoning in Sociology. Boston: Houghton Mifflin.
> (See their "Index of Qualitative Variation")
>
>
> Regards,
>
> Mike Lacy
> Dept. of Sociology
> Colorado State University
> Fort Collins CO 80523-1784
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