Kolm-Index

Der Kolm-Index ist ein Ungleichheitsmaß zur Beschreibung der absoluten Konzentration, das nach dem französischen Ökonomen und Ökonometriker Serge-Christophe Kolm benannt ist.

Definition

Sei $N$ die Anzahl der Einkommen, so dass $N=n\cdot m$ gilt. Hierbei gibt $n$ die Anzahl verschiedener Einkommen an und jedes Einkommen hat $m$ Empfänger (Einkommensbezieher). Die Zahl gleicher Paare mit einem gegebenen Einkommen beträgt:

{\frac {m\cdot (m-1)}{2}}

und die Gesamtanzahl gleicher Einkommen wäre:

{\frac {n\cdot m\cdot (m-1)}{2}}\,.

Offensichtlich wäre die Gesamtzahl aller Paare:

{\frac {N\cdot (N-1)}{2}}-{\frac {n\cdot m\cdot (n\cdot m-1)}{2}}\,.

Dabei kann man an einen ‚Gleichheitsindex‘ in der Form des Terms:

{\frac {n\cdot m\cdot (m-1)}{n\cdot m(n\cdot m-1)}}={\frac {m-1}{N-1}}

denken. Folglich errechnet sich das Ungleichheitsmaß durch Subtraktion von $1$ :

{\frac {1-(m-1)}{N-1}}-{\frac {N-m}{N-1}}={\frac {m\cdot (n-1)}{n\cdot m-1}}={\frac {n\cdot m-m}{n\cdot m-1}}\,.

Wenn das Einkommen $x_{1}$ $f_{i}$ Bezieher hat, lautet der Index wie folgt:

K=1-{\frac {\sum f_{i}^{2}-N}{N\cdot (N-1)}}={\frac {N^{2}-\sum f_{i}^{2}}{N\cdot (N-1)}}\,.

Kolm definierte 1976 den Index folgendermaßen:

K={\frac {1}{\kappa }}\cdot \ln \left[{\frac {1}{n}}\cdot \sum \limits _{i=1}^{n}e^{\kappa \left(\mu -y_{i}\right)}\right]\,;\quad \kappa >0\,,

wobei $\kappa$ die Ungleichheitsaversion angibt.

Motivation

Kolms Intention, diesen kuriosen Index zu entwickeln, begründet sich seiner Meinung nach darin, sich eine Vorstellung davon zu bilden, dass viele simple (Rechen-)Wege bestehen, sich einem Ungleichverteilungsmaß zu nähern.

Literatur

Serge-Christophe Kolm: Unequal inequalities I and II. Journal of Economic Theory 12 u. 13. 1976. S. 416–442 u. 82–111.
Serge-Christophe Kolm: Intermediate measures of inequality. Technical report, CGPC, 1996.

Weblinks

Pramod Kumar Chaubey (eGyanKosh, IGNOU/Indira Gandhi National Open University): Unit 11: Measures of Inequality – PD/gemeinfrei (PDF-Datei; 3,34 MB).

Read other articles:

Paul Felder

American mixed martial arts fighter Paul FelderFelder in 2017BornPaul Robert Felder[1] (1984-04-25) April 25, 1984 (age 39)[1]Philadelphia, Pennsylvania, United StatesNicknameThe Irish DragonHeight5 ft 10 in (178 cm)Weight155 lb (70 kg; 11 st 1 lb)DivisionLightweightWelterweightReach70+1⁄2 in (179 cm)[2]StyleMuay Thai,Shotokan,TaekwondoFighting out ofPhiladelphia, Pennsylvania, United StatesTeamRenzo Gracie Academ...

Player (seri televisi)

PlayerPoster promosiHangul플레이어 GenreLagaKejahatanPembuatStudio Dragon[1]Ditulis olehShin Jae-hyungSutradaraGo Jae-hyunPemeranSong Seung-heonKrystal JungLee Si-eonTae Won-suk [ko]Negara asalKorea SelatanBahasa asliKoreaJmlh. episode14ProduksiProduser eksekutifJinnie ChoiDurasi60 menitRumah produksiiWill Media[1]DistributorOCNRilis asliJaringanOCNFormat gambar1080i (HDTV)Format audioDolby DigitalRilis29 September (2018-09-29) –11 November 2018&#...

GTRE GTX-35VS Kaveri

GTRE GTX-35VS Kaveri adalah turbofan afterburning yang dikembangkan oleh Gas Turbine Research Establishment (GTRE), sebuah laboratorium di bawah DRDO di Bangalore, India. Sebuah desain India, Kaveri pada awalnya ditujukan untuk model produksi kekuatan tempur HAL Tejas, juga dikenal sebagai Light Combat Aircraft (LCA) sedang dibangun oleh Aeronautical Development Agency. Namun, program Kaveri gagal untuk memenuhi persyaratan teknis yang diperlukan atau mengikuti jadwal dibayangkan dan secara ...

Edgar Allan Poe

Disambiguazione – Se stai cercando altri significati, vedi Edgar Allan Poe (disambigua). Disambiguazione – Poe rimanda qui. Se stai cercando altri significati, vedi Poe (disambigua). Edgar Allan Poe nel 1849 Edgar Allan Poe, nato Edgar Poe[1] (Boston, 19 gennaio 1809 – Baltimora, 7 ottobre 1849), è stato uno scrittore, poeta, critico letterario, giornalista, editore e saggista statunitense. Considerato uno dei maggiori e più influenti scrittori statunitensi della stor...

Teuku Muhammad Hasan

Mr.Teuku Muhammad HasanMr. Teuku Muhammad Hasan Gubernur SumatraMasa jabatan1945–1948WakilMohammad Amir PendahuluJabatan BaruPenggantiSutan M. Amin Nasution(Gubernur Sumatera Utara)Mohammad Nasroen(Gubernur Sumatra Tengah)Mohammad Isa(Gubernur Sumatera Selatan)Menteri Pendidikan dan KebudayaanMasa jabatan19 Desember 1948 – 13 Juli 1949 PendahuluAli SastroamidjojoPenggantiSarmidi MangunsarkoroMenteri AgamaMasa jabatan19 Desember 1948 – 13 Juli 1949 PendahuluMasjkurPengg...

Коэффициент теплового расширения

Коэффициент теплового расширения β = 1 V ( d V d T ) p {\displaystyle \beta ={\frac {1}{V}}\left({\frac {dV}{dT}}\right)_{p}} Размерность Θ−1 Единицы измерения СИ К−1 СГС К−1 Коэффицие́нт теплово́го расшире́ния — физическая величина, характеризующая относительное изменение объёма или линейных размер�...

Japan (band)

English new wave band JapanJapan in summer 1981: Sylvian, Jansen, Karn, BarbieriBackground informationAlso known asRain Tree Crow (1989–1991)OriginCatford, South London, EnglandGenres New wave[1] art pop[2][3] glam rock[4] synth-pop[5] post-punk[6] Years active1974–1982, 1989–1991Labels Hansa Virgin Past membersDavid SylvianMick KarnSteve JansenRichard BarbieriRob Dean Japan were an English new wave band formed in 1974 in Catford, South Lo...

Katedral Sarlat

Katedral SarlatKatedral Saint SacerdosPrancis: Cathédrale Saint-Sacerdos de SarlatKatedral SarlatLokasiBayonneNegaraPrancisDenominasiGereja Katolik RomaArsitekturStatusKatedralStatus fungsionalAktifAdministrasiKeuskupanKeuskupan Périgueux Katedral Sarlat (Cathédrale Saint-Sacerdos de Sarlat) adalah sebuah gereja katedral Katolik yang terletak di Sarlat-la -Canéda, Prancis. Itu adalah monumen nasional. Keuskupan Sarlat didirikan pada tahun 1317 dengan sejumlah keuskupan di wilayah ters...

Merlevenez

Merlevenez L'église Notre-Dame-de-Joie. Blason Logo Administration Pays France Région Bretagne Département Morbihan Arrondissement Lorient Intercommunalité Blavet Bellevue Océan Communauté(siège) Maire Mandat Bruno Le Bosser 2020-2026 Code postal 56700 Code commune 56130 Démographie Gentilé Merlevenézien, Merlevenézienne Populationmunicipale 3 203 hab. (2021 ) Densité 181 hab./km2 Population agglomération 218 689 hab. Géographie Coordonnées 47° 4...

Sergei Prikhodko (footballer, born 1984)

Russian footballer For other people named Sergei Prikhodko, see Sergei Prikhodko (disambiguation). Sergei Prihodko Sergei Prikhodko in action for FC SheksnaPersonal informationFull name Sergei Sergeyevich PrihodkoDate of birth (1984-05-09) 9 May 1984 (age 39)Place of birth Leningrad, now St. Petersburg, Russian SFSRHeight 1.90 m (6 ft 3 in)Position(s) GoalkeeperYouth career FC Zenit Saint Petersburg Smena Saint PetersburgSenior career*Years Team Apps (Gls)2001 FC Zenit St....

Constitution of Portugal

Current constitution of Portugal This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Constitution of Portugal – news · newspapers · books · scholar · JSTOR (December 2015) (Learn how and when to remove this message) Constitution of the Portuguese RepublicOverviewJurisdictionPortugalRatified2 April 1976Date ...

National Awami Party

Political party in East and West Pakistan For other uses, see National Awami Party (disambiguation). National Awami Party National People's PartyUrdu nameنیشنل عوامی پارٹیBengali nameন্যাশনাল আওয়ামী পার্টিAbbreviationNAPLeaderAbdul Hamid Khan BhashaniFoundersAbdul Hamid Khan Bhashani and Yar Mohammad KhanFounded1957 (1957)Dacca, East Pakistan, PakistanDissolvedNovember 30, 1967 (1967-11-30)Merger ofAPPSindh Mah...

1773 en musique classique

Chronologies Données clés 1770 1771 1772 1773 1774 1775 1776Décennies :1740 1750 1760 1770 1780 1790 1800Siècles :XVIe XVIIe XVIIIe XIXe XXeMillénaires :-Ier Ier IIe IIIe Chronologies thématiques Art Architecture, Arts plastiques (Dessin, Gravure, Peinture et Sculpture), (), Littérature (), Musique (Classique) et Théâtre Ingénierie (), Architecture et () Politique Droit et () Religion (,) Sci...

Dakoue

Village in Beqaa Governorate, LebanonDakoue Dakoueh, DekwehVillageCountry LebanonGovernorateBeqaa GovernorateDistrictWestern Beqaa DistrictGovernment • MayorRaymond al-GhajarPopulation (2004) • Total800 DakoueShown within LebanonLocation3 kilometres (1.9 mi) southwest of Mejdel Anjar, LebanonCoordinates33°41′42″N 35°53′35″E / 33.69500°N 35.89306°E / 33.69500; 35.89306HistoryPeriodsHeavy Neolithic, Neolithic, RomanCultu...

Falls City, Oregon

City in Oregon, United StatesFalls City, OregonCityFire department in Falls CityLocation in OregonCoordinates: 44°51′58″N 123°26′19″W / 44.86611°N 123.43861°W / 44.86611; -123.43861CountryUnited StatesStateOregonCountyPolkIncorporated1893Government • MayorTJ Bailey[citation needed]Area[1] • Total1.20 sq mi (3.11 km2) • Land1.20 sq mi (3.11 km2) • Water0.00 sq...

Robert Indiana

American artist (1928–2018) Robert IndianaRobert Indiana. Photo by Dennis GriggsBornRobert Clark(1928-09-13)September 13, 1928New Castle, Indiana, U.S.DiedMay 19, 2018(2018-05-19) (aged 89)Vinalhaven, Maine, U.S.NationalityAmericanEducationHerron School of Art and Design, Arsenal Technical High School, Art Institute of Chicago, Skowhegan School of Painting and Sculpture, Edinburgh College of ArtOccupation(s)Artist, theatrical set designer and costume designerWorksLOVEMovementPop art, H...

Guo Ziyi

Guo ZiyiAdipati Dai 代國公Pangeran Fenyang 汾陽王Gambar ini diambil dari sebuah buku berjudul Wan xiao tang - Zhu Zhuang - Hua zhuan (晩笑堂竹荘畫傳) yang diterbitkan hampir 10 tahun setelah berdirinya Republik Tiongkok ((十年), 1921.Kelahiran697Kematian9 Juli 9, 781 (umur 83-84)Nama anumertaZhongwu 忠武AyahGuo Jingzi 郭敬之Anak8 putra, termasuk Guo Ai 郭曖, ayah dari Janda Permaisuri Guo dari TangPekerjaanJenderal Ini adalah nama Tionghoa; marganya adalah Guo. Guo Ziyi ...

皇位継承

この項目では、一般的な天皇の位の継承について説明しています。直近で2019年（平成31年/令和元年）に天皇の退位等に関する皇室典範特例法に基づいて行われた皇位継承については「明仁から徳仁への皇位継承」をご覧ください。諸外国における国王などの位の継承については「王位継承」をご覧ください。第126代天皇今上天皇即位礼正殿の儀2019年（令和元年）10�...

Uniform Crime Reports

Federal Bureau of Investigation program in the United States This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Uniform Crime Reports – news · newspapers · books · scholar · JSTOR (November 2018) (Learn how and when to remove this message) Uniform Crime ReportingActive1929 - presentCountryUnited StatesAgencyFed...

عيون الجواء

هذه المقالة عن مدينة عيون الجواء. لمحافظة عيون الجواء، طالع محافظة عيون الجواء. عيون الجواء الاسم الرسمي عيون الجواء[1] الإحداثيات 26°29′40″N 43°38′07″E / 26.494392°N 43.635247°E / 26.494392; 43.635247 تقسيم إداري البلد السعودية التقسيم الأعلى محافظة عيون الجو...

PROFILPELAJAR.COM