What Is The Formula Of Kurtosis. Excels kurtosis function calculates excess kurtosis. S sample standard deviation.
Kurtosismoment frac1nsumn_i1fracr_i - overlinersigma_P4 Kurtosisexcess frac1nsumn_i1fracr_i - overlinersigma_P4 - 3 Kurtosissample fracnn1n-1n-2n-3sumn_i1fracr_i - overlinersigma_S_P4 Kurtosisfisher fracn1n-1n-2n-3fracsumn_i1fracr_i4nsumn_i1fracr_i2n2 - frac3n-1n1 Kurtosis. Kurtosis sum x-m4Sigma4n I understand n is the population total and not a sample total and I have found some forms of the equation as using n-1 sample statistic. A normal curve has a value of 3 a leptokurtic has beta_2 greater than 3 and platykurtic has beta_2 less then 3.
μ 4 x x 4 N.
Nov 09 2020 The formula for kurtosis calculation is complex 4th moment in the moment-based calculation so we will stick to the concept and its visual clarity. On the Meaning of Kurtosis Kurtosis can be formally defined as the standard- ized fourth population moment about the mean E X - IX4 IX4 132 E X- IX22 04 where E is the expectation operator IX is the mean 114. Therefore sample kurtosis equals. Of course theaverage value of zis always zero but the average value ofz4is always 1 and is larger when you have afew big deviations on either side of the mean than when you have a lotof small ones.
