Detecting AnomaliesbyBenford's Law
digits wastothelogarithmic one.Othermathematicians (S.Goudsmit, W.Furry, H.Hurwitz, R.Pinkham, R.Raimi, Benford's lawgives expected patterns ofthedigits innu- andespecially byT.Hill) gavethetheoretical basis forBenmerical data.Itcanbeusedasa tooltodetect outliers ford's Law. forexample inasatestfortheauthenticity andreliability oftransaction level accounting data.BasedonBenford's lawtests forfirst twodigits, first three digits, last digits, II Mathematical approach lastdigit, last twodigits havebeenderived asanadditional analytical tool. Benford's lawisknownasa 'first Clearly theunderlying premise ofBenford's Law digit law', 'digit analisys' or'Benford-Newcomb phenom-isthatthesubject population ofquantities, expressed in enon'. Thesecond ordertestisananalysis ofthedigitthebase10andmoreorless arbitrary units, will befairly frequencies ofthedifferences between theordered (ranked) evenly distributed ona logarithmic scale. Thisisconvalues inadataset.Thedigit frequencies ofthese difer- firmed bythefactthattheexponents onthese constants encesapproximates thefrequencies ofBenford's Lawforarefairly uniformly distributed (atleast overseveral ormostdistributions oftheoriginal data.Fromsomeaudi-dersofmagnitude). Asaresult, theprobability ofthe tor's pointofviewitisveryimportant ifitispossible to leading digit beingdclearly approaches [4] useBenford 'slawtotrace siginificant changes indatain p dIB 10}loglo (d+ 1) loglo d someperiod oftimeordetect sometrends within them. log10 10- log10d