structural:scholar_edition
Fisher's moment coefficient of skewness

γ 1:= μ ~ 3 = E = μ 3 σ 3 = E (E) 3 / 2 = κ 3 κ 2 3 / 2 {\displaystyle \gamma _{1}:={\tilde {\mu }}_{3}=\operatorname {E} \left={\frac {\mu _{3}}{\sigma ^{3}}}={\frac {\operatorname {E} \left}{\left(\operatorname {E} \left\right)^{3/2}}}={\frac {\kappa _{3}}{\kappa _{2}^{3/2}}}} where μ is the mean, σ is the standard deviation, E is the expectation operator, μ is the third central moment, and κ are the t -th cumulants. It is sometimes referred to as Pearson's moment coefficient of skewness, or simply the moment coefficient of skewness, but should not be confused with Pearson's other skewness statistics (see below). The last equality expresses skewness in terms of the ratio of the third cumulant κ to the 1.5th power of the second cumulant κ. This is analogous to the definition of kurtosis as the fourth cumulant normalized by the square of the second cumulant. The skewness is also sometimes denoted Skew.