skewness coefficient

An alternative skewness coefficient may be derived from the sample mean and the individual observations:

It is one third of the Pearson 2 skewness coefficient and lies between 1 and +1 for any distribution.

The distribution of the skewness coefficient a in large sample sizes ( 45) approaches that of a normal distribution.

For example, in a skewed distribution, the nonparametric skew (and Pearson's skewness coefficients) measure the bias of the median as an estimator of the mean.

Incidentally this formula is also the Pearson mode or first skewness coefficient, and shows that this statistic for a unimodal distribution is bounded by 3.

Although determines the skewness of the distribution, it should not be confused with the typical skewness coefficient or 3rd standardized moment, which in most circumstances is undefined for a geometric stable distribution.

Estimates of the population mode from the sample data may be difficult but the difference between the mean and the mode for many distributions is approximately three times the difference between the mean and the median which suggested to Pearson a second skewness coefficient: