Transcription of A Statistical Distribution Function of Wide Applicability
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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.]]
Charlier and Crama-. Charlier says that, at the first look, the agreement with the normal distribution seems very satisfactory, but that a closer examination shows a small negative skewness and a small posi tive kurtosis. CraIOOr has calculated the values of X'on the hypotheses of normal distribution and asymptotic expansions from it. The
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