# Talk:Theil index

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## 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)

## 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%7C1,0%7C1,0%7C1,0%7C1,0%7C1,0%7C1,0%7C1,0%7C1,0%7C1,1 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)

## 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)

## 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)

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)

## Atkinson Index

The sentence "This can be interpreted in the Theil index as the probability a dollar drawn at random from the population came from a specific individual. This is the same as the first term, the individual's share of aggregate income." is a bit of a problem. Theil's index is a redundancy (The gap between maximumn entropy and effective entropy), so it is in the entropy domain. The operation 1-exp(-Theil) turns it into an Atkinson index, which you can treat as a "probability". --DL5MDA (talk) 01:01, 31 October 2008 (UTC)

## Sloppy writing

Quoting from the article:

The formula[1] is
$T_1=\frac{1}{N}\sum_{i=1}^N \left( \frac{x_i}{\overline{x}} \cdot \ln{\frac{x_i}{\overline{x}}} \right)$
$T_0=\frac{1}{N}\sum_{i=1}^N \left( \ln{\frac{\overline{x}}{x_i}} \right)$
where $x_i$ is the income of the $i$th person, $\overline{x}= \frac{1}{N} \sum_{i=1}^N x_i$ is the mean income, and $N$ is the number of people. The first term inside the sum can be considered the individual's share of aggregate income, and the second term is that person's income relative to the mean.

There are obvious problems with the above:

• We have two expressions: T1 and T2. Which is the Theil index and what is the other one?
• It says "The first term". But the expresssion
$\frac{x_i}{\overline{x}} \cdot \ln{\frac{x_i}{\overline{x}}}$
contains only one term. Could it be that what was meant was "The first factor"?
• Why do people write like that?

Michael Hardy (talk) 22:18, 1 July 2009 (UTC)

## Incorrect TeX

The code W_\mbox{Theil-L} does not have the same effect as W_\text{Theil-L}, in that the first form results in a minus sign and the second in a hyphen. Obviously a hyphen is intended.

The purpose of \mbox is to prevent line-breaks when TeX is used in the usual way, as opposed to the way it's used on Wikipedia. It's not interchangeable with \text. Michael Hardy (talk) 19:37, 15 July 2009 (UTC)

I posted the comment above when Wikipedia was just recovering from about 20 minutes of non-editability, and kept it terse out of impatience. But now it may be working normally. Here are the two appearances:
W_\mbox{Theil-L} $W_\mbox{Theil-L} \,$
W_\text{Theil-L} $W_\text{Theil-L} \,$

The second one is correct. Michael Hardy (talk) 20:41, 15 July 2009 (UTC)

## What is U?

As it stands, the section "What does U mean?" seems like a bit of absurd comedy to me, since I don't see any mention of this mythical U anywhere else in the article. Perhaps somebody who knows something on the subject can clarify this? 92.105.194.250 (talk) 10:25, 8 May 2011 (UTC)

Just checked history of page. Seems like the person who added it hasn't touched the article in any other way. Most likely somebody who edited the wrong article by accident. I'm not at all an expert, but talking about an undefined symbol using terms which are not in any way related to the subject in question (at least with respect to the current article) warrants section deletion. NabilStendardo (talk) 20:34, 19 November 2012 (UTC)

Deleted "Meaning of U" section. Gregorp (talk) 20:16, 27 February 2014 (UTC)

## Conversion to the Atkinson index.

The article currently states that atkinson index with epsilon=0 can be calculated from the thiel-T(a=1). This is plainly wrong, as Atkins index with epsilon=o is equal to zero.

The only known transformation is Theil-s(a=0) to Atkins with e=1, although I can assure you that using A=1-T^-(e*epsilon) from theil-S(a=0) for theil>.1 will yield very close approximations for Atkins index for 2>Epsilon>0 which is the range for actual income distributions. — Preceding unsigned comment added by Kieranlatty (talkcontribs) 20:21, 12 August 2011 (UTC)

## Error in TL Decomposition

Is there not an error in Tl decomposition? The different subgroups should be weighted according to their size, shouldn't they? — Preceding unsigned comment added by 101.5.154.41 (talk) 11:39, 10 December 2013 (UTC)