My Dear you can see attachment file about this question and aslo I'm used JB to link between them

definition of JB criterion like we denoted it in programs in appendix as

JB=n/6(SK2+KU2/4) where sk is skewness and ku is kurtosis

and p_JB (probability of JB criterion )

also you can depend on Matlab as [h,p,jbstat,critval] = jbtest(___)

With Best Regards

Skew and Kurtosis are part of descriptive statistics to help us describe with numbers a distribution of data, like a bell curve.  Imagine a bell curve:

MEAN: where the center of the bell curve is

STANDARD DEVIATION: how wide the bell curve is

SKEW: how much the bell curve is “pushed over” to one side or the other so, rather than being perfectly symmetrical (skew=0), it’s “bunched up” on one side and has a longer tail on the other.

KURTOSIS: how steeply or softly the bell curve comes to it’s “point”

All four properties are independent of each other.

Hope this helps, Srikanth!

Kevin

Histograms summarizing Skewness and Kurtosis:

http://www.epixanalytics.com/modelassist/AtRisk/images/15/image403.gif

thanks to prof. Fadhil Abdulabbas Abidi and prof. Kevin Grobman for your valuable response.

prof. Kevin, your brief explanation is really excellent. it is wonderful to summarize four descriptive statistics in one sentence for each. you are really great.

NO, there is no relationship between skew and kurtosis. They are measuring different properties of a distribution. There are also higher moments. The first moment of a distribution is the mean, the second moment is the standard deviation, the third is skew, the fourth is kurtosis. There are fifth, and higher moments, but I haven't seen them used nor do they have a special name.

https://en.wikipedia.org/wiki/Moment_(mathematics)

http://www.aip.de/groups/soe/local/numres/bookcpdf/c14-1.pdf

https://ocw.mit.edu/resources/res-tll-004-stem-concept-videos-fall-2013/videos/probability-and-statistics/moments-of-distributions/