\(\text{Kurtosis}\)

You can use the \(\text{Kurtosis}\) function to calculate the excess Kurtosis of a collection of values.

You can use the \kurtosis backslash command to insert this function.

The following variants of this function are available:

  • \(\text{real } \text{Kurtosis} \left ( \ldots \right )\)

Note that this function works for all data types and, like the \(\text{Average}\) and \(\text{Count}\) functions can recursively traverse iterable types to locate scalar values to include in the excess kurtosis calculation.

The excess kurtosis is calculated by:

\[\text{Kurtosis} \left ( X \right ) = \left [ \frac{1}{N} \sum_{ x \in X } \left ( \frac{ x - \mu }{\sigma} \right ) ^ 4 \right ] - 3\]

Figure 163 shows the basic use of the \(\text{Kurtosis}\) function.

../_images/kurtosis_example.png

Figure 163 Example Use Of The Kurtosis Function