▁The ▁Lor enz ▁curve ▁is ▁a ▁probability ▁plot ▁( a ▁P – P ▁plot ) ▁comparing ▁the ▁distribution ▁of ▁a ▁parameter ▁in ▁a ▁population ▁against ▁a ▁hypoth et ical ▁uniform ▁distribution ▁of ▁that ▁parameter . ▁It ▁can ▁usually ▁be ▁represented ▁by ▁a ▁function ▁L ( F ), ▁where ▁F , ▁the ▁cum ulative ▁portion ▁of ▁the ▁population , ▁is ▁represented ▁by ▁the ▁horizontal ▁axis , ▁and ▁L , ▁the ▁cum ulative ▁portion ▁of ▁the ▁total ▁wealth ▁or ▁income , ▁is ▁represented ▁by ▁the ▁vertical ▁axis . ▁ ▁For ▁a ▁population ▁of ▁size ▁n , ▁with ▁a ▁sequence ▁of ▁values ▁y i , ▁i ▁= ▁ 1 ▁to ▁n , ▁that ▁are ▁indexed ▁in ▁non - de cre asing ▁order ▁( ▁y i ▁ ≤ ▁y i + 1 ), ▁the ▁Lor enz ▁curve ▁is ▁the ▁continuous ▁piece wise ▁linear ▁function ▁connecting ▁the ▁points ▁( ▁F i , ▁Li ▁), ▁i ▁= ▁ 0 ▁to ▁n , ▁where ▁F 0 ▁= ▁ 0 , ▁L 0 ▁= ▁ 0 , ▁and ▁for ▁i ▁= ▁ 1 ▁to ▁n : ▁ ▁For ▁a ▁discrete ▁probability ▁function ▁f ( y ), ▁let ▁y i , ▁i ▁= ▁ 1 ▁to ▁n , ▁be ▁the ▁points ▁with ▁non - zero ▁prob abilities ▁indexed ▁in ▁increasing ▁order ▁( ▁y i ▁< ▁y i + 1 ). ▁ ▁The ▁Lor enz ▁curve ▁is ▁the ▁continuous ▁piece wise ▁linear ▁function ▁connecting ▁the ▁points ▁( ▁F i , ▁Li ▁), ▁i ▁= ▁ 0 ▁to ▁n , ▁where ▁F 0 ▁=