calculate kurtosis in matlab and minitab but not same answer

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Amir Azadeh Ranjbar
Amir Azadeh Ranjbar on 13 Dec 2021
Edited: dpb on 13 Dec 2021
it my data
0.53767 -1.30769 -1.34989 -0.20497
1.83389 -0.43359 3.03492 -0.12414
-2.25885 0.34262 0.72540 1.48970
0.86217 3.57840 -0.06305 1.40903
0.31877 2.76944 0.71474 1.41719
Kmatlab=kurtosis(x(:,2))=1.4069
but in minitab
kurtosis(x(:,2))=-2.37
??????

Answers (1)

dpb
dpb on 13 Dec 2021
Edited: dpb on 13 Dec 2021
Looks like Minitab uses the bias-corrected estimator with the "-3" convention applied --
K>> kurtosis(x(:,2),0)
ans =
0.63
K>> 3-2.37
ans =
0.63
K>> 0.63-3
ans =
-2.37
K>>
With the default for the optional flag default in MATLAB (==1), then you get the result you got.
See the 'Algorithms' section of the documentation for full details.
With only 5 observations and that the estimator of K uses sum((x-xBar).^4), the random variation in the estimator is quite high and I wouldn't put much faith at all i such a statistic as far as making any judgement from it.

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