# Would you tell me the code for Fisher Pearson skewness?

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Chris on 20 Sep 2022
Commented: Sim on 27 Nov 2023
Would you tell me the code for Fisher Pearson skewness?
How can I get the skewness with Fisher Pearson formula..?

David Goodmanson on 21 Sep 2022
Edited: David Goodmanson on 21 Sep 2022
Hi Chris,
y = rand(1,100); % some data
m = mean(y);
n = numel(y);
scalc = (sum((y-m).^3)/n)/var(y,1)^(3/2)
s = skewness(y)
scalc agrees with Matlab's skewness function.
You have to be careful using the variance here (or the standard deviation). The var default is
sum((y-m)^2)/(n-1)
but for variance as used in Matlab's skewness function, you divide by n instead of (n-1). That means using var(y,1) rather than the default var(y). Same idea for std if that were used.

Walter Roberson on 20 Sep 2022
FPskewness = sum(x - mean(x)) / numel(x) / std(x).^3
You would need to be more rigourous if you wanted to handle non-vectors.
John D'Errico on 21 Sep 2022
Jeff is correct. Skewness would be a scaled (normalized) 3rd central moment, so there MUST be a cube in there.
Sim on 27 Nov 2023
Hi, what should be changed, in the @Walter Roberson formula, to make it correct? I do not understand...
y = rand(1,100); % some data
m = mean(y);
n = numel(y);
s = skewness(y) % matlab embedded function
s = -0.2898
scalc = (sum((y - m).^3) / numel(y)) / var(y,1)^(3/2) % David Goodmanson solution
scalc = -0.2898
FPskewness = sum(y - mean(y)) / numel(y) / std(y).^3 % Walter Roberson solution
FPskewness = -8.9461e-16

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