\(\text{Kurtosis}\)¶
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 166 shows the basic use of the \(\text{Kurtosis}\) function.