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I added more content throughout the article to explain. Also, you're correct about the first term being wrong. It should have been the first factor. Someone else corrected that awhile ago. (Why do people write like that? You have the answer already: they are sloppy.) See if it makes more sense now.
1374:
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
593:
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 I know that Theil wrote at least one monograph, but it is surely out of date, if not out of print.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
608:
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
446:): 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. --
414:
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
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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.
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1359:
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?
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I posted the comment above when
Knowledge 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:
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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?
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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". --
1010:
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.
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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.
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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.
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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: -->
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286:
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
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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.
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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?
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755:{\displaystyle T_{1}={\frac {1}{N}}\sum _{i=1}^{N}\left({\frac {x_{i}}{\overline {x}}}\cdot \ln {\frac {x_{i}}{\overline {x}}}\right)}
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Is there not an error in Tl decomposition? The different subgroups should be weighted according to their size, shouldn't they?
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is a hack in the scripting language Lua which could yield the Theil index for many countries. For further explanation:
404:{\displaystyle GE(\theta )={\frac {1}{\theta ^{2}-\theta }}({\frac {1}{n}}\sum {\frac {y_{i}}{y_{mean}}}^{\theta }-1)}
442:
yields 2.3 for example. But one remark on "only a single person earns everything". Theil's index is a redundancy (
1220:
I would appreciate having someone check what I did to the article, as I hope my modifications are all accurate.--
440:
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
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Would be nice to see a theil index map of the world. Thanks. --Francesco 17:11, 14 August 2007 (UTC)
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As written in the map, some of the compounds of the sum can be negative. But the sum is positive. --
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859:{\displaystyle T_{0}={\frac {1}{N}}\sum _{i=1}^{N}\left(\ln {\frac {\overline {x}}{x_{i}}}\right)}
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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science data. I also see that Jamie
Galbraith's group at UT has been quite active in this area.
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many very negative numbers which also suggests that the above is a typo. What am I missing?
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1114:{\displaystyle {\frac {x_{i}}{\overline {x}}}\cdot \ln {\frac {x_{i}}{\overline {x}}}}
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question (at least with respect to the current article) warrants section deletion.
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The purpose of \mbox is to prevent line-breaks when TeX is used in the usual way,
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contains only one term. Could it be that what was meant was "The first factor"?
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https://www.statisticshowto.datasciencecentral.com/u-statistic-theils/
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http://economicsbulletin.vanderbilt.edu/2008/volume15/EB-07O10036A.pdf
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https://www.statisticshowto.datasciencecentral.com/u-statistic-theils/
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the way it's used on
Knowledge. It's not interchangeable with \text.
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1412:.1 will yield very close approximations for Atkins index for 2: -->
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983:{\displaystyle {\overline {x}}={\frac {1}{N}}\sum _{i=1}^{N}x_{i}}
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0 which is the range for actual income distributions.
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http://luaforge.net/frs/?group_id=49&release_id=794
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1040:. Which is the Theil index and what is the other one?
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http://luaforge.net/frs/shownotes.php?release_id=794
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1328:{\displaystyle W_{\text{Theil-L}}\,}
1297:{\displaystyle W_{\mbox{Theil-L}}\,}
184:This article is within the scope of
95:This article is within the scope of
38:It is of interest to the following
1553:Low-importance Statistics articles
1468:Correct formula and meaning of 'U'
14:
1538:Mid-importance Economics articles
1404:Conversion to the Atkinson index.
1476:. The "U" stands for unbiased.
1389:Deleted "Meaning of U" section.
247:How to interpret the Theil index
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1132:Why do people write like that?
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1486:15:46, 12 December 2018 (UTC)
1462:11:39, 10 December 2013 (UTC)
1399:20:16, 27 February 2014 (UTC)
1385:20:34, 19 November 2012 (UTC)
276:21:38, 9 September 2007 (UTC)
256:21:28, 23 December 2006 (UTC)
198:and see a list of open tasks.
109:and see a list of open tasks.
90:Business and economics portal
1472:Here's the correct Formula:
1230:10:35, 5 February 2018 (UTC)
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459:Theil index map of the world
1548:B-Class Statistics articles
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1340:The second one is correct.
1150:I tried to fix that today,
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451:05:26, 29 August 2007 (UTC)
431:19:40, 28 August 2007 (UTC)
267:05:26, 29 August 2007 (UTC)
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141:project's importance scale
1442:Error in TL Decomposition
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990:is the mean income, and
261:The Theil index is : -->
1370:10:25, 8 May 2011 (UTC)
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171:
165:
162:
159:
155:
142:
138:
132:
129:
128:
125:
108:
104:
100:
99:
91:
85:
80:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
1509:
1498:
1490:
1471:
1454:101.5.154.41
1448:— Preceding
1445:
1417:— Preceding
1413:Epsilon: -->
1410:
1407:
1388:
1373:
1358:
1339:
1252:
1250:
1241:
1239:
1188:Theil's L =
1159:Theil's T =
1135:
1034:
1027:
1023:
1017:
627:
607:
592:
488:
462:
413:
285:
253:68.59.91.207
250:
225:
185:
136:
96:
40:WikiProjects
1423:Kieranlatty
919:th person,
1527:Categories
1491:References
1355:What is U?
262:= zero. --
201:Statistics
192:statistics
164:Statistics
1222:FeralOink
112:Economics
103:Economics
59:Economics
1450:unsigned
1431:contribs
1419:unsigned
1022:We have
489:Thanks,
1391:Gregorp
1319:Theil-L
1287:Theil-L
428:Mateoee
228:on the
139:on the
30:B-class
872:where
611:DL5MDA
581:DL5MDA
476:DL5MDA
448:DL5MDA
273:DL5MDA
264:DL5MDA
36:scale.
525:into
485:abs()
417:radek
1482:talk
1458:talk
1427:talk
1395:talk
1381:talk
1366:talk
1346:talk
1261:talk
1226:talk
1141:talk
1033:and
615:talk
1242:not
1024:two
220:Low
131:Mid
1529::
1484:)
1460:)
1433:)
1429:•
1397:)
1383:)
1368:)
1348:)
1263:)
1228:)
1143:)
1106:¯
1087:
1084:ln
1081:⋅
1075:¯
951:∑
932:¯
836:¯
827:
824:ln
799:∑
742:¯
723:
720:ln
717:⋅
711:¯
670:∑
617:)
474:--
393:−
388:θ
350:∑
331:θ
328:−
319:θ
303:θ
1480:(
1456:(
1425:(
1393:(
1379:(
1364:(
1344:(
1315:W
1282:W
1259:(
1224:(
1201:0
1197:T
1172:1
1168:T
1154:.
1139:(
1103:x
1097:i
1093:x
1072:x
1066:i
1062:x
1038:2
1035:T
1031:1
1028:T
998:N
976:i
972:x
966:N
961:1
958:=
955:i
945:N
942:1
937:=
929:x
907:i
885:i
881:x
853:)
845:i
841:x
833:x
820:(
814:N
809:1
806:=
803:i
793:N
790:1
785:=
780:0
776:T
749:)
739:x
733:i
729:x
708:x
702:i
698:x
691:(
685:N
680:1
677:=
674:i
664:N
661:1
656:=
651:1
647:T
613:(
566:|
561:|
539:|
534:|
513:)
510:(
507:s
504:b
501:a
399:)
396:1
380:n
377:a
374:e
371:m
367:y
361:i
357:y
345:n
342:1
337:(
323:2
314:1
309:=
306:)
300:(
297:E
294:G
232:.
143:.
42::
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