# Are kurtosis and skewness meaningful for comparing distributions such as gamma distributions with very pronounced shape parameters? Are kurtosis and skewness meaningful for comparing distributions such as gamma distributions with very pronounced shape parameters? For instance, take the red distribution in the first plot here:

https://en.wikipedia.org/wiki/Gamma_distribution

I have two datasets for which the histogram plots look very similar to each other and to that (red) pdf. When I compute the kurtosis and skewness, however, the values are very different. Applying Kolgomorov-Smirnov tests for the equality of distributions, however, strongly fails to reject the null of equality (p-value is 0.27). I am bit puzzled by the apparent failure of kurtosis and skewness...

• The "red" distribution you single out on the Wikipedia page (not a helpful citation for those who struggle with red and green) is that special case of the gamma known as the exponential. It has a skewness of 2 and kurtosis of 9, which aren't especially large. But you'd get useful intuition for how those measures behave in samples of the size you have by simulation. @whuber's comments thus apply specifically as well as generally. Kolmogorov-Smirnov [NB spelling] is in my view not nearly so useful here as a quantile-quantile plot. – Nick Cox Jul 12 '16 at 23:52
• @Glen_b I have 20 bins in intervals of 5%. For the subsample, the kurtosis is 4.38 and skewness is 1.97. for the sample, the skewness is 1.29 and kurtosis is 1.13. I think that the difference in Kurtosis is quite pronounced, am I correct? – Daniel Pinto Jul 13 '16 at 0:23
• For count proportions I wouldn't consider a gamma as an example -- maybe a scaled binomial (or mixture of scaled binomials). What are the sample sizes of the individual proportions? – Glen_b Jul 13 '16 at 1:35
• Comments are not for extended discussion; this conversation has been moved to chat. – whuber Jul 13 '16 at 13:21