Pareto Distribution - Corporate Finance Institute

The Pareto Distribution is used in describing social, scientific, and geophysical phenomena in society. Pareto created a mathematical formula in ... Home›Resources›Knowledge›Economics›ParetoDistribution ParetoDistribution The"80-20Rule" Writtenby CFITeam UpdatedMay10,2021 WhatisParetoDistribution? TheParetoDistributionwasnamedafterItalianeconomistandsociologistVilfredoPareto.ItissometimesreferredtoastheParetoPrincipleorthe80-20Rule.TheParetoDistributionisusedindescribingsocial,scientific,andgeophysicalphenomenainsociety.Paretocreatedamathematicalformulaintheearly20thcenturythatdescribedtheinequalitiesinwealthdistributionthatexistedinhisnativecountryofItaly. Paretoobservedthat80%ofthecountry’swealthwasconcentratedinthehandsofonly20%ofthepopulation.Thetheoryisnowappliedinmanydisciplinessuchasincomes,productivity,populations,andothervariables.TheParetodistributionservestoshowthatthelevelofinputsandoutputsisnotalwaysequal. HistoryofParetoDistribution TheParetoDistributionprinciplewasfirstemployedinItalyintheearly20thcenturytodescribethedistributionofwealthamongthepopulation.In1906,VilfredoParetointroducedtheconceptoftheParetoDistributionwhenheobservedthat20%ofthepeapodswereresponsiblefor80%ofthepeasplantedinhisgarden. HerelatedthisphenomenontothenatureofwealthdistributioninItaly,andhefoundthat80%ofthecountry’swealthwasownedbyabout20%ofitspopulation.Intermsoflandownership,theItalianobservedthat80%ofthelandwasownedbyahandfulofwealthycitizens,whocomprisedabout20%ofthepopulation. ThedefinitionoftheParetoDistributionwaslaterexpandedinthe1940sbyDr.JosephM.Juran,aprominentproductqualityguru.JuranappliedtheParetoprincipletoqualitycontrolforbusinessproductiontoshowthat20%oftheproductionprocessdefectsareresponsiblefor80%oftheproblemsinmostproducts. AccordingtoJuran,focusingonthe20%causesofdefectsallowedorganizationstoimplementmoreeffectivequalitycontrolmeasuresandmakebetteruseoftheirresources.Juran’sadditionstotheParetodistributionconceptwerecontainedinhis1951booktitled“QualityControlHandbook.” ParetoDistributionFormula TheformulaforcalculatingtheParetoDistributionisasfollows: F(x)=1–(k/x)α Where: x–Randomvariable k –Lowerboundondata α–Shapeparameter Onachart,theParetodistributionisrepresentedbyaslowlydecliningtail,asshownbelow: Source:WikipediaCommons Thechartisdefinedbythevariablesαandx.Itprovidestwomainapplications.Oneoftheapplicationsistomodelthedistributionofwealthamongindividualsinacountry.Thechartshowstheextenttowhichalargeportionofwealthinanycountryisownedbyasmallpercentageofthepeoplelivinginthatcountry. Thesecondapplicationistomodelthedistributionofcitypopulations,wherealargepercentageofthepopulationisconcentratedintheurbancentersandaloweramountintheruralareas.Thepopulationinurbancenterscontinuestoincreasewhiletheruralpopulationcontinuestodeclineasyoungermembersofthepopulationmigratetourbancenters. PracticalApplicationsoftheParetoDistribution 1.BusinessManagement OneoftheapplicationsoftheParetoconceptisinbusinessmanagement.Abusinessmayobservethat20%oftheeffortdedicatedtoaspecificbusinessactivitygenerates80%ofthebusinessresults.Abusinesscanusethisratiotoidentifythemostimportantsegmentsthatitcanfocusonandtherebyincreaseitsefficiency. Forexample,ifmarketingcontributedtoincreasedbusinessresults,thebusinesscanallocatemoretimeandresourcestomarketingactivitiestoincreasethecompany’srevenuesandprofits. 2.CompanyRevenues The80-20Paretorulemayalsoapplyinevaluatingthesourceofthecompanyrevenues.Forexample,whenthecompanyobservesthat80%ofreportedannualrevenuescomefrom20%ofitscurrentcustomers,itcanfocusitsattentiononincreasingthecustomersatisfactionofinfluentialcustomers. Fromthisobservation,thecompanycanalsodeducethat80%ofcustomercomplaintscomefrom20%ofcustomerswhoformthebulkofitstransactions.Also,focusingonsolvingthecomplaintsof20%ofitscustomerscanincreasetheoverallcustomersatisfactionofthecompany.Thecompanyshouldfocusonretaining20%ofitsinfluentialcustomersandonacquiringnewcustomers. 3.EmployeeEvaluation Acompanycanalsousethe80-20ruletoevaluatetheperformanceofitsemployees.Thecompanymayobservethat80%ofitsoveralloutputisthedirectresultofabout20%ofitsemployees.Usingtheratio,thecompanycanfocusonrewardingthe20%mostproductiveemployeesasawayofmotivatingthemandencouragingthelowerclusterofemployeestoworkharder.Theproductivityratiocouldalsoshowthecompanythat80%ofhumanresourceproblemsarecausedby20%ofthecompany’semployees. LimitationsoftheParetoDistribution Whilethe80-20Paretodistributionruleappliestomanydisciplines,itdoesnotnecessarilymeanthattheinputandoutputmustbeequalto100%.Forexample,20%ofthecompany’scustomerscouldcontribute70%ofthecompany’srevenues.Theratiobringsatotalof90%.It showsthattheParetoconceptismerelyanobservationthatsuggeststhatthecompanyshouldfocusoncertaininputsmorethanothers. AdditionalResources CFIistheofficialprovideroftheFinancialModelingandValuationAnalyst(FMVA)® certificationprogram,designedtotransformanyoneintoaworld-classfinancialanalyst. Tokeeplearninganddevelopingyourknowledgeoffinancialanalysis,wehighlyrecommendtheadditionalCFIresourcesbelow: Externality KeyPerformanceIndicators(KPI) NormativeEconomics Sustainability FinancialAnalystCertification BecomeacertifiedFinancialModelingandValuationAnalyst (FMVA)®bycompletingCFI’sonlinefinancialmodelingclasses! 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