The form of the sampling distribution of sample mean of random sample from a normal probability distribution is known. Similarly, the form of the sampling distribution of sample variance of random sample from a normal probability distribution is also known. However, it is not known to me whether the forms of sampling distributions of (i) measure of skewness and (ii) measure of kurtosis of random sample from a normal probability distribution available.
Here the question is
"Are the forms of sampling distributions of measures of skewness and kurtosis of random sample from a normal probability distribution available ? "
The best reference I could find was this link:
https://www.google.com/search?q=sampling+distribution+soreness+kurtosis&client=firefox-b&oq=sampling+distribution+soreness+kurtosis&gs_l=mobile-heirloom-serp.12...5239.24209.0.29763.19.17.0.2.2.0.171.1722.11j6.17.0....0...1c.1.34.mobile-heirloom-serp..9.10.897.huLjcRfqD2A
Best wishes, David Booth
I have gone through the references through the link provided by David Eugene Booth.
The sampling distributions of skewnss and kurtosis are available there for large sample. The sampling distributions mentioned there are the consequences of the central limit theorem which states that the sampling distributions of skewnss and kurtosis for large sample are asymptotically normal.
However, I have not found any result about the sampling distributions of skewnss and kurtosis for small sample. Thus, the answer of the question
"Are the sampling distributions of skewnss and kurtosis for small sample available ? "
is still not known to me.
@ DC
May not available !
Check the pdf in following link:
http://clinchem.aaccjnls.org/content/clinchem/35/2/330.full.pdf