Lee ebe Foster Greer Thorbecke si

{{Databox}}'''Indices''' '''Foster–Greer–Thorbecke''' bụ ezinụlọ nkemetrik ịda ogbenye . The kasị eji index si ezinụlọ, ''FGT <sub>2</sub>'', na-etinye elu arọ na ịda ogbenye nke ndị kasị daa ogbenye ndị mmadụ n'otu n'otu, na-eme ka ọ a jikọtara ụfọdụ nke ịda ogbenye na ego inequality na a na-ewu ewu nhọrọ n'ime mmepe aku na uba . Ewebata indices na akwụkwọ 1984 site n'aka ndị ọkachamara n'ihe banyere akụ na ụba Erik Thorbecke, [[Joel Greer]], na James Foster . <ref>{{Cite journal|author=Foster|first=James|title=A class of decomposable poverty measures|journal=[[Econometrica]]|year=1984|volume=52|issue=3|pages=761–766|doi=10.2307/1913475}}</ref> <ref>{{Cite journal|title=The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later|author=James Foster|date=28 May 2010|journal=The Journal of Economic Inequality|doi=10.1007/s10888-010-9136-1|volume=8|issue=4|pages=491–524}}</ref>

A na-enweta indices n'otu n'otu n'ime ezinaụlọ site n'ịgbanwe ụkpụrụ dị iche iche nke paramita ''α'' n'ime usoro ndị a:

<math>FGT_\alpha=\frac {1} {N} \sum_{i=1}^H \left(\frac {z-y_i} {z}\right)^\alpha </math>

ebe ''z'' bụ ọnụ ụzọ ịda ogbenye, ''N'' bụ ọnụ ọgụgụ ndị mmadụ na akụ na ụba, ''H'' bụ ọnụ ọgụgụ ndị ogbenye (ndị nwere ego na ma ọ bụ n'okpuru ''z'' ), ''y <sub>i</sub>'' bụ ego nke onye ọ bụla ''i.'' Ọ bụrụ <math>\alpha</math> dị ala mgbe ahụ FGT metric arọ ndị niile nwere ego n'okpuru z roughly otu. Ka ọnụ ahịa ''α dị elu dị elu,'' ebe ịdị arọ na-abawanye na ndị kasị daa ogbenye. Ka ọnụ ọgụgụ FGT dị elu, ka ịda ogbenye na-abawanye na akụ na ụba.

== FGT <sub>0</sub> na FGT <sub>1</sub> ==
Site na ''α'' = 0, usoro ahụ na-ebelata na ọnụ ọgụgụ isi : ọnụ ọgụgụ nke ndị bi n'okpuru ịda ogbenye.

<math>FGT_0=\frac {H} {N}</math>

Site na ''α'' = 1, usoro ahụ na-ebelata ka ọ bụrụ ntụpọ ịda ogbenye .

<math>FGT_1=\frac {1} {N} \sum_{i=1}^H \left(\frac {z-y_i} {z}\right) </math>

Enwere ike idegharị ''FGT <sub>1</sub>'' dị ka:

<math>FGT_1=\frac {H} {N} \left(\frac {z-\bar{y}_p} {z}\right) </math> ,

ebee <math>\bar{y}_p=\sum_{i=1}^H\frac {y_i} {H}</math> bụ nkezi ego nke ndị ogbenye. Ya mere, ''FGT <sub>1</sub>'' nwere ike igosipụta dị ka ngwaahịa nke ''FGT <sub>0</sub>'' na nkezi ego ọdịiche nke ndị ogbenye.

== FGT <sub>2</sub> ==
Ọ bụ ezie na a na-eji ndepụta ndetu abụọ a belatara ọtụtụ ebe, ndepụta FGT kachasị na mmepe akụ na ụba bụ ụdị ''α'' = 2, nke bụ oke kacha ala (n'ozuzu) iji tụọ ahaghị nhata ego yana ịda ogbenye.

<math>FGT_2=\frac {1} {N} \sum_{i=1}^H \left(\frac {z-y_i} {z}\right)^2 </math>

Enwere ike idegharị ''FGT <sub>2</sub>'' dị ka:

<math>FGT_2=\frac {H} {N} [\mu^2 + (1-\mu^2) C_v^2]</math>

ebe ''C <sub>v</sub>'' bụ ọnụọgụ mgbanwe n'etiti ego ndị ogbenye, ''H'' bụ ọnụ ọgụgụ ndị ogbenye, na ''μ'' bụ nke:

<math>\mu=\frac {1} {H}\sum_{i=1}^H \left(\frac {z-y_i} {z}\right) </math> .

Ndị ọzọ decompositions nke index nwekwara ike.  Naanị nha na-ejikọta ''FGT <sub>0</sub>'', ''FGT <sub>1</sub>'', na [[Gini coefficient|Gini index]] bụ [[Sen Index|Sen index]] . </link><sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">&#x5B; ''[[wikipedia:Tinye edensibịa|<span title="This claim needs references to reliable sources. (August 2014)">a chọrọ nkọwa</span>]]'' &#x5D;</sup>

Na Meksiko, a na-eji ụdị ndeksi a wepụta ego gọọmentị etiti n'etiti mpaghara maka mmemme mmụta, ahụike na nri na-erite uru ndị ogbenye. Na 2010, Gọọmenti Mexico nakweere a multidimensional ịda ogbenye ihe dabere na a variant nke FGT ụfọdụ nke a ga-eji na ezubere iche nke oke nke mmadụ ego ka ndị ogbenye ezinụlọ na obodo larịị. <ref>{{Cite web|url=http://www.economics.cornell.edu/et17/ET-Short%20bio%202013.doc}}</ref>

== Ihe ndetu ==
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[[Òtù:Pages with unreviewed translations]]