[[Estimator]]
# Sample excess kurtosis

Let $\{ X_{j} \}_{j=1}^n$ be a sample of [[Independence of random variables|independent and identically distributed]] [[Real random variable|real random variables]] with [[Expectation|mean]] $\mu$ and [[Standard deviation|variance]] $\sigma^2$.
The **sample excess kurtosis** is #m/def/prob 
$$
\begin{align*}
 \frac{\frac{1}{n}\sum_{j=1}^n(X_{j}- \overline{X}_{n})^4}{S^4_{n}} -3
\end{align*}
$$
where $S_{n}^2$ is the [[Sample variance]].
This estimates the [[Excess kurtosis]] of a sample.


#
---
#state/tidy | #lang/en | #SemBr