a8cd9fe3-f8fc-4b2c-aef5-ca45db39c630 16 7 10 false true 0 decimal

&[DATE] &[TIME] - &[FILENAME]

matlab definition: https://www.mathworks.com/help/stats/skewness.html

Skewness/Kurtosis of a vector

Y skewness2 m Y Mean : n Y rows : i 1 n range Num i el Y i el m - (3^: Den i el Y i el m - (2^: 21 line for result 1 n / Num sum (* 1 n / Den sum (* sqrt 3^/ : 41 line :

matlab definition: https://www.mathworks.com/help/stats/kurtosis.html

Y kurtosis2 m Y Mean : n Y rows : i 1 n range Num i el Y i el m - (4^: Den i el Y i el m - (2^: 21 line for k1 1 n / Num sum (* 1 n / Den sum (* (2^/ : 41 line :

From Matlab Kurtosis page:

Note

Some definitions of kurtosis subtract 3 from the computed value, so that the normal distribution has kurtosis of 0. The kurtosis function does not use this convention.

Note

Some definitions of kurtosis subtract 3 from the computed value, so that the normal distribution has kurtosis of 0. The kurtosis function does not use this convention.

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As defined by Jean

Y skewness1 m Y Mean : n Y rows : i 1 n range Num i el Y i el m - (3^: 11 line for n Num sum (* n 1 - (n 2 - (* Y StdDev (3^* / 41 line :

With Mathcad Kurtosis function, normal distribution has kurtosis of 0. This is same as Kurtosis Excess in SMATH

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Y kurtosis1 m Y Mean : n Y rows : i 1 Y rows range V i el Y i el Y Mean - (4^: V V sum : 21 line for n n 1 + (* V * n 1 - (n 2 - (* n 3 - (* Y StdDev (4^* / 3 n 1 - (2^* n 2 - (n 3 - (* / - 41 line :

Y 0.43 0.22 0.26 0.48 0.49 0.01 0.40 0.30 0.14 0.23 0.24 0.58 0.33 0.11 0.03 0.34 0.15 0.36 181 mat :

ADDING 3 to kurtosis1 to match Matlab/SMath version of Kurtosis

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sanity Mathcad Y skewness1 Y skewness2 Y Skewness Y kurtosis1 Y KurtosisExcess Y kurtosis1 3 + Y kurtosis2 Y Kurtosis 81 mat 0.0053 0.0048 0.0048 0.618 - 0.775 - 2.382 2.225 2.225 81 mat

n Y rows : 18

skew_err 72 Zeros : kurt_err 72 Zeros : 21 line

sample_size 10100200300400500100071 mat :

n 17 range Y sample_size n el eval Random : s1 Y Skewness : s2 Y skewness1 : s3 Y skewness2 : k1 Y Kurtosis : k2 Y kurtosis1 : k3 Y kurtosis2 : skew_err n 1 el s1 s3 - s1 / : skew_err n 2 el s1 s2 - s1 / : kurt_err n 1 el k1 k3 - s1 / : kurt_err n 2 el k1 k2 3 + (- s1 / : 111 line for

ADD 3 to kurtosis1 function.

skew_err Matlab Skew Error(%) Mathcad Skew Error(%) Samples 13 mat 100 skew_err * sample_size augment stack :

kurt_err Matlab Skew Error(%) Mathcad Skew Error(%) Samples 13 mat 100 kurt_err * sample_size augment stack :

skew_err Matlab Skew Error(%) Mathcad Skew Error(%) Samples 3.290176 1012 -^* 18.58541 - 10 9.690764 1012 -^* - 1.52933 - 100 2.718164 1012 -^* - 0.7572593 - 200 1.186732 1011 -^* 0.5032157 - 300 4.90164 1011 -^* 0.3768058 - 400 6.602458 1012 -^* 0.3011546 - 500 2.209584 1012 -^* 0.1502881 - 100083 mat

kurt_err Matlab Skew Error(%) Mathcad Skew Error(%) Samples 0 5.8999 - 10 4.0306 1011 -^* - 6.532 1000 1.5436 200 6.5852 1011 -^* 9.2044 - 300 1.0452 1011 -^* 0.6832 400 5.1595 1012 -^* - 1.1915 500 8.4501 1011 -^* 0.4107 - 100083 mat