Sample excess kurtosis

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 excess kurtosis is prob

1 𝑛 \sum 𝑛 𝑗 = 1 (𝑋 𝑗 - ―― 𝑋 𝑛) 4 𝑆 4 𝑛 - 3

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