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A Statistical Distribution Function of Wide Applicability

AStatisticalDistributionFunctionofWideAp plicabilityByWALODDIWEIBULL,lSTOCKHOLM, ,lst'VlD2thisconditionI .FavariableXisattributedtotheindividuals ofapopula~ion, thedistributionfunction(df)ofdenotedF(x) ,maybedefinedasthenumberofallindividuals havinganX~x, ,andthuswehaveP(X~x)=F(x)[1]F(x)=1-e(x-x u)mXI.[51 Anydistributioniunctionmaybewritteninthe form(1p)n=e-nrp(x)..[3]Theonlymeritofthi sdfistobefoundinthefactthatitsimplestmat hematicalexpressionoftheappropriateform, tion[2J, ,inmanycases, ~ ' ,appliedtorealpopulationsfromnaturalbiol ogicalfields, ,itutterlyhopelesstoexpectatheoreticalba sisfordistributionfunctionsofrandomvaria blessuchasstrengthofma-terialsorofmachin epartsorparticlethe"Dl~rtlCJ~~S"flyash,C yrtoideae,orevenadultmales, , [5],hasbeennotonlytopopulations,forwhich itwasoriginallyalsotopopulationsfromwide lydifferentfields,and, ,"~:l.]]

Ifthe classes 17-18are pooled, the value of X' - 4.50, and the doff9 - 31/, - 51/ , give a P - 0.56. It may be of interest to compare this result with those of Charlier and Crama-. Charlier says that, at the first look, the agreement with the normal distribution seems very satisfactory, but that a closer

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