# Uncertainty of Sample skew and kurtosis

What is the uncertainty of a samples skewness and kurtosis? Such as the uncertainty of the standard deviation is SD/sqrt(2*(N-1)). I was able to find what someone is calling the Standard Error of these but they both only depend on N which doesn't make sense to me.

Skewness Standard Error: sqrt((N^2-1)/((N-3)*(N+5)))

Kurtosis Standard Error: SSE*sqrt(6*N*(N-1)/((N-2)*(N+1)*(N+3)))

These get close to 1 in the range of measurements that I'm looking at which doesn't have the same behavior of the uncertainty of the standard deviation, which goes from inf to 0 with increasing measurements. And it doesn't depend on the value of the skew or kurtosis...

Turns out the terms I were looking for are either the variance of sample skewness and kurtosis, or standard deviation of skewness or kurtosis. I have found the following:

Std. Dev. of Skewness: sqrt((6*(N-2)*(Std. Dev.)^2)/((N+1)*(N+3)))
Std. Dev. of Kurtosis: sqrt((24*N*(N-2)*(N-3)*(Std. Dev.)^2)/((N+1)^2*(N+3)*(N+5)));

I hope these are correct as they seem rather obscure (which I can see by the fact no one answered) though I'd think they should be much more well known.

Stephen Tashi