A Note on Skewness and Kurtosis

Abstract

A simple proof is given of the inequality $\alpha_4\ge\alpha_3^2+1$, where $\alpha_3$ and $\alpha_4$ are the third and fourth moments for zero mean and unit variance. Also, an upper bound $(N-2)/(N-1)^{\frac{1}{2}}$ for $\alpha_3$ is derived, $N$ being the sample size.