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Is there a minimum number of observations in order to assess concentration or not?

kjetil b halvorsen
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adrCoder
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No. One observation belonging to one category has Herfindahl index $\sum_{j=1}^1 p_j^2 = 1$. That may be too extreme to be interesting or useful, but there is nothing invalid about the calculation.

Writing about the Herfindahl index stamps someone (usually) as an economist. Let's assume that proportions or probabilities of categories $p_j$ add to $1$ over $j = 1, \dots, J$ categories and the measure being calculated is $\sum p_j^2$. If you are using its complement or reciprocal, that's fine, but some details need changing. This measure has many origins and Herfindahl's proposal in economics was just one of many, the idea going at least to Gini about 40 years earlier.

Nick Cox
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  • interesting. are there any good books / papers worth reading related to these topics? – adrCoder Jul 10 '20 at 18:47
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    There is an enormous if repetitive literature spread across economics, ecology, etc., etc. Under other names this measure (or its complement) crops up again and again: under people's names like Gini or Simpson, or under direct names like match probability, repeat rate or quadratic diversity. David Aldous packs a lot into one page or so in a posting accessible from http://isi.cbs.nl/bnews/11a/index.html – Nick Cox Jul 11 '20 at 07:17