## KURTOSIS

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.

### Syntax

Result = KURTOSIS(X [, /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

#### 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. (See Special Floating-Point Values for more information on IEEE floating-point values.)

### 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
```

Introduced: 5.1