96:
deaths per 100,000. Effects of the index were also found for infant mortality (P = 0.013); coronary heart disease (P = 0.004); malignant neoplasms (P = 0.023); and homicide (P < 0.001). Strong associations were also found between the index and causes of death amenable to medical intervention. The Gini coefficient showed very little correlation with any of the causes of death.
871:
60:
If, instead, the Hoover is divided by the percentage of the total national income received by the people getting less than their equal-share (i.e. less than the mean income), then that gives the percentage by which those people, as a group, would get more than they currently do, if income were equal.
87:
which is based on the summation, over all income-ordered population-percentiles, of the cumulative income up to each percentile. That sum is divided by the maximum value that it could have (its value with complete equality), to express it as a percentage of its maximum-possible value. The result is
95:
Results: The Robin Hood index was positively correlated with total mortality adjusted for age (r = 0.54; P < 0.05). This association remained after adjustment for poverty (P < 0.007), where each percentage increase in the index was associated with' an increase in the total mortality of 21.68
56:
If the Hoover is divided by the percentage of the population whose income is less than their equal-share (i.e. the mean income), that gives the average cost of that Hoover-value, per person whose income is less than their equal-share. ...that cost being expressed in terms of the national mean
100:
The Gini, like the Theil (below), is an impartial measure of inequality over the entire population. That can be of interest and use, but the Robin Hood differs, as a not-impartial examination of the total amount by which members of the population get less than their equal-share.
668:
709:
314:
42:
The Hoover Index can be calculated by the following subtraction: The percentage of the people getting less than their equal-share (i.e. less than the national mean income), minus their percentage of the national income.
547:
91:
A report from the
National Library of Medicine, of the National Institute of Health, described a statistical study that compared how the Robin Hood and the Gini are correlated with mortality:
496:
449:
866:{\displaystyle T_{s}={\frac {1}{2}}\sum _{i=1}^{N}\ln {\frac {{E}_{i}}{{A}_{i}}}\left({\frac {{E}_{i}}{{E}_{\text{total}}}}-{\frac {{A}_{i}}{{A}_{\text{total}}}}\right).}
183:
701:
422:
395:
134:
539:
516:
469:
368:
340:
203:
154:
210:
50:(which graphs cumulative income vs cumulative population (income-ordered population-percentile)and the 45 degree line representing perfect equality).
663:{\displaystyle H={\frac {1}{2}}\sum _{i=1}^{N}\left|{\frac {{E}_{i}}{{E}_{\text{total}}}}-{\frac {{A}_{i}}{{A}_{\text{total}}}}\right|.}
39:
i.e. The Hoover is the total amount (as a percentage of the national-income) by which people have less than their equal income-share.
1092:
70:...i.e. dividing the percentage of the population whose income is less than the mean by their percentage of the national income.
67:
That latter cost can also be gotten by dividing, instead of subtracting, the two numbers that were subtracted to get the Hoover.
53:
It would be informative to express the Hoover in terms of its average cost to individuals who get less than their equal-share:
877:
33:
1116:
1047:
1034:
988:
Inequality
Measures in Mathematical Programming for the Air Traffic Flow Management Problem with En-Route Capacities
940:"Income distribution and mortality: Cross sectional ecological study of the Robin Hood index in the United States"
1070:
Income distribution and mortality: cross sectional ecological study of the Robin Hood index in the United States
64:...in other words the cost, to them, of that Hoover value, expressed in terms of their actual current income.
1096:
1121:
474:
427:
909:
899:
986:
The notation using E and A follows the notation of a small calculation published by
Lionnel Maugis:
1100:
80:(SES) and health. It is conceptually one of the simplest inequality indices used in econometrics.
159:
679:
400:
373:
112:
77:
8:
1061:
32:. It is equal to the percentage of the total population's income that would have to be
964:
939:
524:
501:
454:
353:
325:
188:
139:
309:{\displaystyle H={\frac {1}{2}}{\frac {\sum _{i}|x_{i}-{\bar {x}}|}{\sum _{i}x_{i}}}.}
1043:
1030:
969:
29:
1069:
959:
951:
84:
1053:
894:
889:
46:
It can be graphically represented as the longest vertical distance between the
1088:
955:
1110:
47:
973:
424:
could be the amount (absolute or relative) of earners in the quantile #i.
1004:
1000:
919:
914:
674:
904:
350:. Thus, inequities can be computed for quantiles with different widths
347:
343:
319:
1067:
Bruce P Kennedy, Ichiro
Kawachi, Deborah Prothrow-Stith (1996)
76:
The Hoover index is typically used in applications related to
673:
For comparison, here also the computation of the symmetrized
937:
938:
Kennedy, B. P.; Kawachi, I.; Prothrow-Stith, D. (1996).
322:. For the formula, a notation is used, where the amount
83:
A more frequently encountered inequality measure is the
1074:
1022:, Review of Economics and Statistics, 18, No. 162–71
712:
682:
550:
527:
504:
477:
457:
430:
403:
376:
356:
328:
213:
191:
162:
142:
115:
88:
subtracted from one, to get a measure of inequality.
1050:(Describes about 50 different inequality measures.)
865:
695:
662:
533:
510:
490:
463:
443:
416:
389:
362:
334:
308:
197:
177:
148:
128:
1108:
498:would be the sum of the income earners in all
1103:) for Atkinson, Gini, and Hoover inequalities
397:could be the income in the quantile #i and
1020:The Measurement of Industrial Localization
999:For an explanation of the comparison with
185:be the mean income. Then the Hoover index
963:
451:then would be the sum of incomes of all
1109:
318:This value can also be computed using
1027:An Introduction to Regional Economics
521:Computation of the Robin Hood index
13:
1012:
14:
1133:
1081:
491:{\displaystyle A_{\text{total}}}
444:{\displaystyle E_{\text{total}}}
346:only appears as upper border of
1025:Edgar Malone Hoover Jr. (1984)
1018:Edgar Malone Hoover Jr. (1936)
36:to make all the incomes equal.
993:
980:
931:
274:
267:
244:
169:
104:
1:
876:Both formulas can be used in
1087:Free Inequality Calculator:
7:
944:BMJ (Clinical Research Ed.)
883:
73:...and then subtracting 1.
10:
1138:
1039:Philip B. Coulter: (1989)
178:{\displaystyle {\bar {x}}}
1117:Income inequality metrics
956:10.1136/bmj.312.7037.1004
910:Income inequality metrics
900:Generalized entropy index
925:
878:spreadsheet computations
867:
756:
697:
664:
587:
535:
512:
492:
465:
445:
418:
391:
364:
336:
310:
199:
179:
150:
130:
98:
990:(für IFORS 96), 1996
868:
736:
698:
696:{\displaystyle T_{s}}
665:
567:
536:
513:
493:
466:
446:
419:
417:{\displaystyle A_{i}}
392:
390:{\displaystyle E_{i}}
365:
337:
311:
200:
180:
151:
136:be the income of the
131:
129:{\displaystyle x_{i}}
93:
1093:downloadable scripts
1041:Measuring Inequality
710:
680:
548:
525:
502:
475:
455:
428:
401:
374:
354:
326:
211:
189:
160:
140:
113:
78:socio-economic class
20:, also known as the
1062:Scientific American
950:(7037): 1004–1007.
863:
693:
660:
531:
508:
488:
461:
441:
414:
387:
360:
332:
306:
289:
242:
195:
175:
146:
126:
28:, is a measure of
1122:Welfare economics
853:
850:
822:
819:
789:
734:
650:
647:
619:
616:
565:
534:{\displaystyle H}
511:{\displaystyle N}
485:
464:{\displaystyle N}
438:
363:{\displaystyle A}
335:{\displaystyle N}
301:
280:
270:
233:
228:
198:{\displaystyle H}
172:
149:{\displaystyle i}
30:income inequality
1129:
1007:
997:
991:
984:
978:
977:
967:
935:
872:
870:
869:
864:
859:
855:
854:
852:
851:
848:
846:
840:
839:
834:
828:
823:
821:
820:
817:
815:
809:
808:
803:
797:
790:
788:
787:
782:
776:
775:
770:
764:
755:
750:
735:
727:
722:
721:
702:
700:
699:
694:
692:
691:
669:
667:
666:
661:
656:
652:
651:
649:
648:
645:
643:
637:
636:
631:
625:
620:
618:
617:
614:
612:
606:
605:
600:
594:
586:
581:
566:
558:
540:
538:
537:
532:
517:
515:
514:
509:
497:
495:
494:
489:
487:
486:
483:
470:
468:
467:
462:
450:
448:
447:
442:
440:
439:
436:
423:
421:
420:
415:
413:
412:
396:
394:
393:
388:
386:
385:
369:
367:
366:
361:
341:
339:
338:
333:
315:
313:
312:
307:
302:
300:
299:
298:
288:
278:
277:
272:
271:
263:
257:
256:
247:
241:
231:
229:
221:
204:
202:
201:
196:
184:
182:
181:
176:
174:
173:
165:
155:
153:
152:
147:
135:
133:
132:
127:
125:
124:
85:Gini coefficient
22:Robin Hood index
1137:
1136:
1132:
1131:
1130:
1128:
1127:
1126:
1107:
1106:
1084:
1064:, December 2005
1058:Sick of Poverty
1054:Robert Sapolsky
1015:
1013:Further reading
1010:
998:
994:
985:
981:
936:
932:
928:
895:Diversity index
886:
847:
842:
841:
835:
830:
829:
827:
816:
811:
810:
804:
799:
798:
796:
795:
791:
783:
778:
777:
771:
766:
765:
763:
751:
740:
726:
717:
713:
711:
708:
707:
687:
683:
681:
678:
677:
644:
639:
638:
632:
627:
626:
624:
613:
608:
607:
601:
596:
595:
593:
592:
588:
582:
571:
557:
549:
546:
545:
526:
523:
522:
503:
500:
499:
482:
478:
476:
473:
472:
456:
453:
452:
435:
431:
429:
426:
425:
408:
404:
402:
399:
398:
381:
377:
375:
372:
371:
370:. For example,
355:
352:
351:
327:
324:
323:
294:
290:
284:
279:
273:
262:
261:
252:
248:
243:
237:
232:
230:
220:
212:
209:
208:
190:
187:
186:
164:
163:
161:
158:
157:
156:-th person and
141:
138:
137:
120:
116:
114:
111:
110:
107:
12:
11:
5:
1135:
1125:
1124:
1119:
1105:
1104:
1083:
1082:External links
1080:
1079:
1078:
1065:
1051:
1037:
1023:
1014:
1011:
1009:
1008:
1003:'s index see:
992:
979:
929:
927:
924:
923:
922:
917:
912:
907:
902:
897:
892:
890:Atkinson index
885:
882:
874:
873:
862:
858:
845:
838:
833:
826:
814:
807:
802:
794:
786:
781:
774:
769:
762:
759:
754:
749:
746:
743:
739:
733:
730:
725:
720:
716:
690:
686:
671:
670:
659:
655:
642:
635:
630:
623:
611:
604:
599:
591:
585:
580:
577:
574:
570:
564:
561:
556:
553:
530:
507:
481:
471:quantiles and
460:
434:
411:
407:
384:
380:
359:
331:
305:
297:
293:
287:
283:
276:
269:
266:
260:
255:
251:
246:
240:
236:
227:
224:
219:
216:
194:
171:
168:
145:
123:
119:
106:
103:
9:
6:
4:
3:
2:
1134:
1123:
1120:
1118:
1115:
1114:
1112:
1102:
1098:
1094:
1090:
1086:
1085:
1076:
1072:
1071:
1066:
1063:
1059:
1055:
1052:
1049:
1048:0-8133-7726-9
1045:
1042:
1038:
1036:
1035:0-07-554440-7
1032:
1028:
1024:
1021:
1017:
1016:
1006:
1002:
996:
989:
983:
975:
971:
966:
961:
957:
953:
949:
945:
941:
934:
930:
921:
918:
916:
913:
911:
908:
906:
903:
901:
898:
896:
893:
891:
888:
887:
881:
879:
860:
856:
843:
836:
831:
824:
812:
805:
800:
792:
784:
779:
772:
767:
760:
757:
752:
747:
744:
741:
737:
731:
728:
723:
718:
714:
706:
705:
704:
688:
684:
676:
657:
653:
640:
633:
628:
621:
609:
602:
597:
589:
583:
578:
575:
572:
568:
562:
559:
554:
551:
544:
543:
542:
528:
519:
505:
479:
458:
432:
409:
405:
382:
378:
357:
349:
345:
329:
321:
316:
303:
295:
291:
285:
281:
264:
258:
253:
249:
238:
234:
225:
222:
217:
214:
206:
192:
166:
143:
121:
117:
102:
97:
92:
89:
86:
81:
79:
74:
71:
68:
65:
62:
58:
54:
51:
49:
44:
40:
37:
35:
34:redistributed
31:
27:
23:
19:
1068:
1057:
1040:
1026:
1019:
995:
987:
982:
947:
943:
933:
875:
672:
520:
317:
207:
108:
99:
94:
90:
82:
75:
72:
69:
66:
63:
59:
55:
52:
48:Lorenz curve
45:
41:
38:
26:Schutz index
25:
21:
18:Hoover index
17:
15:
1077:312:1004–07
1005:Theil index
1001:Henri Theil
920:Theil index
915:Suits index
675:Theil index
518:quantiles.
105:Computation
1111:Categories
905:Gini index
703:is given:
348:summations
825:−
761:
738:∑
622:−
569:∑
344:quantiles
320:quantiles
282:∑
268:¯
259:−
235:∑
170:¯
1029:, 1984,
884:See also
57:income.
1056:(2005)
974:8616345
965:2350807
24:or the
1097:Python
1089:Online
1046:
1033:
972:
962:
926:Notes
849:total
818:total
646:total
615:total
484:total
437:total
1099:and
1091:and
1044:ISBN
1031:ISBN
970:PMID
205:is:
109:Let
16:The
1101:Lua
1075:BMJ
960:PMC
952:doi
948:312
342:of
1113::
1073:,
1060:,
968:.
958:.
946:.
942:.
880:.
758:ln
541::
1095:(
976:.
954::
861:.
857:)
844:A
837:i
832:A
813:E
806:i
801:E
793:(
785:i
780:A
773:i
768:E
753:N
748:1
745:=
742:i
732:2
729:1
724:=
719:s
715:T
689:s
685:T
658:.
654:|
641:A
634:i
629:A
610:E
603:i
598:E
590:|
584:N
579:1
576:=
573:i
563:2
560:1
555:=
552:H
529:H
506:N
480:A
459:N
433:E
410:i
406:A
383:i
379:E
358:A
330:N
304:.
296:i
292:x
286:i
275:|
265:x
254:i
250:x
245:|
239:i
226:2
223:1
218:=
215:H
193:H
167:x
144:i
122:i
118:x
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