# Kurtosis

March 29, 2018

Back to: Random Testing

The kurtosis of a set of numbers, *x _{n}*,

*n*= 1, …,

*N*, is given in Equation 8:

(1)

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 *k * – 3. The value of the excess kurtosis for a Normal distribution is zero.