Kurtosis

March 29, 2018

The kurtosis of a set of numbers, xnn = 1, …, N, is given in Equation 8:

(1)   \begin{equation*} \kappa=\frac{1}{N\sigma^2}\sum_{n=1}^{N}(x_{n}-\mu)^4 \cong \frac{\frac{1}{N} \sum_{n=1}^{N} (x_{n}-\bar{x})^4}{(\frac{1}{N} \sum_{n=1}^{N} (x_{n}-\bar{x})^2)^2} \end{equation*}

Equation 8

The kurtosis is a measure of the average fourth power of the deviation of a signal from its mean value divided by the fourth power of the standard deviation. Therefore, it is dimensionless. For a random variable with a Normal distribution the kurtosis has a value of 3 (see the lesson on Normal (Gaussian) Distribution). The turbulent pressure signal shown in Figure 3.3 has a kurtosis value of 2.6.

It should be noted that some computer programs calculate the excess kurtosis value which is  – 3. The value of the excess kurtosis for a Normal distribution is zero.