▁The ▁Lor enz ▁curve ▁is ▁not ▁defined ▁if ▁the ▁mean ▁of ▁the ▁probability ▁distribution ▁is ▁zero ▁or ▁infinite . ▁ ▁The ▁Lor enz ▁curve ▁for ▁a ▁probability ▁distribution ▁is ▁a ▁continuous ▁function . ▁ ▁However , ▁Lor enz ▁curves ▁representing ▁dis continu ous ▁functions ▁can ▁be ▁constructed ▁as ▁the ▁limit ▁of ▁Lor enz ▁curves ▁of ▁probability ▁distributions , ▁the ▁line ▁of ▁perfect ▁inequality ▁being ▁an ▁example . ▁ ▁The ▁information ▁in ▁a ▁Lor enz ▁curve ▁may ▁be ▁summar ized ▁by ▁the ▁G ini ▁coefficient ▁and ▁the ▁Lor enz ▁asym met ry ▁coefficient . ▁ ▁The ▁Lor enz ▁curve ▁cannot ▁rise ▁above ▁the ▁line ▁of ▁perfect ▁equality . ▁▁ ▁If ▁the ▁variable ▁being ▁measured ▁cannot ▁take ▁negative ▁values , ▁the ▁Lor enz ▁curve : ▁cannot ▁sink ▁below ▁the ▁line ▁of ▁perfect ▁inequality , ▁is ▁increasing . ▁Note ▁however ▁that ▁a ▁Lor enz ▁curve ▁for ▁net ▁worth ▁would ▁start ▁out ▁by ▁going ▁negative ▁due ▁to ▁the ▁fact ▁that ▁some ▁people ▁have ▁a ▁negative ▁net ▁worth ▁because ▁of ▁deb t . ▁ ▁The ▁Lor enz ▁curve ▁is ▁invariant ▁under ▁positive ▁scaling . ▁ ▁If ▁X ▁is ▁a ▁random ▁variable , ▁for ▁any ▁positive ▁number ▁c ▁the ▁random ▁variable ▁c ▁X ▁has ▁the ▁same ▁Lor enz ▁curve ▁as ▁X . ▁ ▁The ▁Lor enz ▁curve ▁is ▁f li pped ▁twice , ▁once ▁about ▁F ▁= ▁ 0 . 5 ▁and ▁once ▁about ▁L ▁= ▁ 0 . 5 , ▁by ▁neg ation . ▁ ▁If ▁X ▁is ▁a ▁random ▁variable ▁with ▁Lor enz ▁curve ▁L X (