Kurtosis

March 29, 2018

Kurtosis is a measure of the average fourth power of a signal’s deviation from its mean value divided by the fourth power of the standard deviation. Equation 8 gives the kurtosis of a set of numbers, xnn = 1, …, N.

(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

Kurtosis is dimensionless. For a random variable with normal distribution, the kurtosis has a value of 3 (visit the lesson Normal (Gaussian) Distribution.) The turbulent pressure signal 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.