Talk:Theil index

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[edit] How to interpret the Theil index

This article is unclear on how to interpret a Thiel index value. It seems that zero is absolute equality, and large positive values indicate large inequality, but what do negative values mean? 68.59.91.207 21:28, 23 December 2006 (UTC)

The Theil index is >= zero. --DL5MDA 05:26, 29 August 2007 (UTC)
As written in the map, some of the compounds of the sum can be negative. But the sum is positive. --DL5MDA 21:38, 9 September 2007 (UTC)

[edit] Starting from the generalized entropy measure

i have another Question: How can one compute the theil index starting from the generalized entropy measure? I have a Formula wich states General entropy GE(\theta)= \frac{1}{\theta ^{2}-\theta}(\frac{1}{n}\sum {\frac{y_{i}}{y_{mean}}}^{\theta}-1) and that if a take 1 for theta i will bekome the Theil index. But if i do this i will become 0 times... =0 ???? so whats wrong? can someone help?

I think you have to take the limit as theta goes to 1. The part I'm confused about is that the article states that "If one person has all the income, then the index = lnN.", but if one person has all the income then other persons' income is zero and ln (0) = - infinity, not ln N. Also the map has many very negative numbers which also suggests that the above is a typo. What am I missing?radek 21:19, 5 April 2007 (UTC)

In information theory, it is defined that 0*log(0) = 0, based on the fact that x*log(x) approaches zero as x goes to zero. So, when all of the income is earned by a single person, the Shannon entropy (S) is zero, leaving only the ln(N) part of the index. Mateoee 19:40, 28 August 2007 (UTC)
http://www.poorcity.richcity.org/calculator/?quantiles=1,0|1,0|1,0|1,0|1,0|1,0|1,0|1,0|1,0|1,1 yields 2.3 for example. But one remark on "only a single person earns everything". Theil's index is a redundancy (http://en.wikipedia.org/wiki/Theil_index#_note-6): Maximum entropy minus actual entropy. Here the maximum entropy stays. - And one remark on such examples: In physics, one would not apply statistical physics anymore on such situations. If one works with entropy concepts in econometrics, one should have a larger number of people to deal with. --DL5MDA 05:26, 29 August 2007 (UTC)

[edit] Theil index map of the world

Would be nice to see a theil index map of the world. Thanks. --Francesco 17:11, 14 August 2007 (UTC)

http://luaforge.net/frs/?group_id=49&release_id=794 is a hack in the scripting language Lua which could yield the Theil index for many countries. For further explanation: http://luaforge.net/frs/shownotes.php?release_id=794 --DL5MDA 05:26, 29 August 2007 (UTC)

[edit] abs()

Thanks, Michael Hardy, for changing abs() into | | . I recolored the | | in order to draw attention to the fact, that the difference between the symmetrized Theil and the Hoover index just is the operation (coloured in blue) on the deviations from equity. DL5MDA 22:41, 16 October 2007 (UTC)

[edit] References, please

Would someone please supply at least one reference to a monography or journal article discussing this topic? I know that Theil wrote at least one monograph, but it is surely out of date, if not out of print. Incidentally, I share Theil's fascination with the application of Shannon entropy to social science data. I also see that Jamie Galbraith's group at UT has been quite active in this area.132.181.160.42 04:49, 9 November 2007 (UTC)