Sample skewness

Let ${𝑋 𝑗} 𝑛 𝑗 = 1$ be a sample of independent and identically distributed real random variables with mean $𝜇$ and variance $𝜎 2$ . The sample skewness is prob

1 𝑛 \sum 𝑛 𝑗 = 1 (𝑋 𝑗 - ―― 𝑋 𝑛) 3 𝑆 3 𝑛

where $𝑆 2 𝑛$ is the Sample variance. This estimates the Skewness of a sample.