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The <b>Kurva Lorenz curve</b> wasdiwangun developed byku [[Max O. Lorenz]] assalaku agrapik graphicalnu representation ofngagambarkeun kateusaruaan[[income]] inequality. ItKurva canbisa alsodipake beoge usedkeur tongukur measure inequality ofkateusaruaan [[asset]]s or otheratawa [[distribution]]s sejenna.
Dina diskusi panghasilan pribadi, urang remen nyebutkeun yen, "duapuluh persen sahandapeun sakabeh rumahtangga mibanda sapuluh persen total pangahasilan". Kurva Lorenz dumasar kana ieu ''pernyataan''; unggal titik dina kurva ngagambarkeun unggal ''pernyataan''.
In discussions of personal income, we frequently make statements such as, "the bottom twenty percent of all households have ten percent of the total income". The Lorenz curve is based on such statements; every point on the curve represents one such statement.
The Lorenz [[curve]] isLorenz angarupakeun [[graph of a function|graph]] thatnu showsnembongkeun, fordi the bottomhandap x% of householdsrumahtangga, the percentagepersentase y% of the total income whichpanghasilan theyno havedipibanda. ThePersentase percentagerumah of householdstangga isdi plottedplot ondina thesumbu x axis, thepersentasi percentagepanghasilan ofdina income on thesumbu y axis.
Sebaran panghasilan persis sarua di masarakat bakal jadi hiji dimana unggal jalma mibanda panghasilan nu sarua. Dina kasus ieu, handapeun N% masarakat bakal salawasna mibanda N% panghasilan. Mangka sebaran nu persis sarua digambarkeun ku garis lempeng y=x; bisa disebut yen ieu garis ngarupakeun garis persis sarua.
A perfectly equal income distribution in a society would be one in which every person has the same income. In this case, the bottom N% of society would always have N% of the income. Thus a perfectly equal distribution can be depicted by the straight line y=x; we call this line the line of perfect equality.
ASebaran perfectlynu inequalpersis distributionteusarua, bysacara contrastjelas, wouldnyaeta besaurang oneboga inkabeg whichpenghasilan onesarta personnu hassejenna allteu theboga income and everyone else has nonenanaon. InDina thatkasus caseeta, thekurva curvebakal would be atdina y=0 forkeur allsakabrh x<100, andsarta y=100 whenwaktu x=100. We callGaris thisdina curvekurva theieu linedisebut ofgaris perfectkateusaruaan inequalitysampurna.
Catetan yen dumasar kana panghasilan (atawa naon bae nu bakal diukur) teu bisa negatip, mangka teu mungkin keur kurva Lorenz naek di saluhureun garis sarua sampurna, atawa nurun sahandapeun garis teusarua sampurna. Kurva kudu naek sarta [[concave]].
Note that providing that incomes (or whatever else is being measured) cannot be negative, it is impossible for the Lorenz curve to rise above the line of perfect equality, or sink below the line of perfect inequality. The curve must be increasing and [[concave]].
Kurva Lorenz dipeke keur ngitung [[koefisien Gini]], numana daerah antara garis sampurna jeung kurva, salaku persentasi daerah antara garis sarua sampurna jeung garis teu sarua sampurna.
The Lorenz curve is used to calculate the [[Gini coefficient]], which is the area between the line of perfect equality and the Lorenz curve, as a percentage of the area between the line of perfect equality and the line of perfect inequality.
ATipikal typicalkurva Lorenz curvebisa looksditempo likedi thishandap ieu:
[[image:lorenz-curve1.png]]
* [[Welfare economics]]
* [[Income inequality metrics]]
* [[GiniKoefisien coefficientGini]]
* [[Social welfare (political science)]]
* [[ROC analysis]]
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