Would you tell me the code for Fisher Pearson skewness?

Would you tell me the code for Fisher Pearson skewness?

How can I get the skewness with Fisher Pearson formula..?

Answer 1

[David Goodmanson]

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.

Answer 2

[Walter Roberson]

FPskewness = sum(x - mean(x)) / numel(x) / std(x).^3

You would need to be more rigourous if you wanted to handle non-vectors.

[Jeff Miller]

That doesn't look quite right since sum(x-mean(x)) equals 0. Maybe it should be this?

FPskewness = sum( (x - mean(x)).^3 ) / numel(x) / std(x)^3

[Walter Roberson]

@Jeff Miller

You could be right; I do find a site that has the ^3 as you indicate. But the initial site I found (which I cannot seem to locate now) and https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/skewness.htm define it as

[Jeff Miller]

OK, but surely that's wrong because the numerator of that g_1 is zero for any vector of x's.

[John D'Errico]

Jeff is correct. Skewness would be a scaled (normalized) 3rd central moment, so there MUST be a cube in there.

[Sim]

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