Just calculate the skew and kurtosis? There are moment definitions for them which only require knowing the values of previous moments, so they are easy to calculate (and most languages like R and Julia have a command for calculating the skew and kurtosis from a data vector).

Are you instead asking how to interpret it? If that's the case, I like to use Gamma distributions. You can easily adjust the two parameters of the Gamma distribution to find a Gamma with similar skew. That gives a rough idea of how your skewed distribution looks. Same for kurtosis (using a t-distribution)

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http://brownmath.com/stat/shape.htm#Skewness

http://brownmath.com/stat/shape.htm#Kurtosis

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Hi Saddaf,

another interesting link (but less comprehensive than the previous) ishttps://www.spcforexcel.com/knowledge/basic-statistics/are-skewness-and-kurtosis-useful-statistics .

About kurtosis

http://stats.stackexchange.com/questions/172589/should-we-teach-kurtosis-in-an-applied-statistics-course-if-so-how

If your question is related to a normal distribution of data there's an interesting discussion of some years ago on ResearchGate

https://www.researchgate.net/post/What_is_the_acceptable_range_of_skewness_and_kurtosis_for_normal_distribution_of_data

and, then, this reference about programming: http://stats.stackexchange.com/questions/35348/how-to-determine-whether-data-is-slightly-or-extremely-non-normally-distributed.

Hope this helps

Marco  

Thanks all for the help and providing in detail information with references. I am actually done with Skewness and Kurtosis, I am only confused about classifying the distribution either moderately, highly or approximately skewed. 

I found one rule of thumb in a link http://brownmath.com/stat/shape.htm#Skew_CI

provided in Fabrice's answer. Following is the rule of thumb:

• If skewness is less than −1 or greater than +1, the distribution is highly skewed.
• If skewness is between −1 and −½ or between +½ and +1, the distribution is moderately skewed.
• If skewness is between −½ and +½, the distribution is approximately symmetric.

If I use this rule of thumb, I can classify but I am not able to find the relevant literature also stating this rule. This will then not support my work. Anyone can help me to find the references.

Thanks and Have a good day

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rules of thumb are by definition somewhat aritrary and therefore do not really need strong grounding in references to prior work !

(moreover, books stating such "rules of thumb" always give the same caveat : "it is somewhat arbitrary, use at your own risks" !)

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anyway, if you want to hide behind a reference, here is one :

An Introduction to Statistical Concepts: Third Edition

Richard G. Lomax,Debbie L. Hahs-Vaughn

Routledge / Taylor and Francis 2012

pp 89-91

you'll note that their "rules of thumb" are more liberal than Brown U's one ...

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screen copies from a google book query :