The KURTOSIS function computes the statistical kurtosis of an *n*-element vector. Kurtosis is defined as the degree to which a statistical frequency curve is peaked. KURTOSIS calls the IDL function MOMENT.

**Note: **KURTOSIS subtracts 3 from the raw kurtosis value since 3 is the kurtosis for a Gaussian (normal) distribution. For resulting values, positive values of the kurtosis (leptokurtic) indicate pointed or peaked distributions. Negative values (platykurtic) indicate flattened or non-peaked distributions.

## Examples

`; Define the n-element vector of sample data:`

x = [65, 63, 67, 64, 68, 62, 70, 66, 68, 67, 69, 71, 66, 65, 70]

`; Compute the kurtosis:`

`result = KURTOSIS(x)`

`; Print the result:`

`PRINT, result`

IDL prints

`-1.18258`

## Syntax

*Result* = KURTOSIS(*X*
[, DIMENSION=*value*]
[, /DOUBLE] [, /NAN] )

## Return Value

Returns the floating point or double precision statistical kurtosis. If the variance of the vector is zero, the kurtosis is not defined, and KURTOSIS returns !VALUES.F_NAN as the result.

## Arguments

### X

An *n*-element, floating-point or double-precision vector.

## Keywords

### DIMENSION

Set this keyword to a scalar indicating the dimension across which to calculate the kurtosis. If this keyword is not present or is zero, then the kurtosis is computed across all dimensions of the input array. If this keyword is present, then the kurtosis is only calculated only across a single dimension. In this case the result is an array with one less dimension than the input.

### DOUBLE

If this keyword is set, computations are performed in double precision arithmetic.

### NAN

Set this keyword to cause the routine to check for occurrences of the IEEE floating-point values *NaN* or *Infinity* in the input data. Elements with the value *NaN* or *Infinity* are treated as missing data.

## Version History

5.1 |
Introduced |

8.0 |
Added DIMENSION keyword |

## See Also

MEAN, MEANABSDEV, MOMENT, STDDEV, SKEWNESS, VARIANCE