S5 Skewness

The third moment of any standardized random variable X is called the SKEWNESS of X. It is often said that this measures the lack of symmetry, and the existence of tails on right or left. This is true for very simple unimodal distributions with density uniformly declining away from the single mode. However, there are many asymmetric distributions for which the third moment is zero. Also, many distributions which are very close to symmetric have skewness measure very strongly negative or positive. For these reasons, it is best to think of the Pearson Moment Coefficient of Skewness as just a colorful name for the third standardized moment, not to be taken literally. There exist better measures of lack of symmetry, although we do not deal with them in this course.

For the Normal Distribution, the Skewness measure is 0. For the Gamma distribution, it can be computed with the help of the above formulae. Students should compute it as an exercise.

Wikipedia: Skewness — Article provides the original of the image displayed above, and further details on skewness.