## MOMENT

The MOMENT function computes the mean, variance, skewness, and kurtosis of a sample population contained in an n-element vector X. When x = (x0, x1, x2, ..., xn-1), the various moments are defined as follows:

This routine is written in the IDL language. Its source code can be found in the file `moment.pro` in the `lib` subdirectory of the IDL distribution.

### Return Value

If the vector contains n identical elements, MOMENT computes the mean and variance, and returns the IEEE value NaN for the skewness and kurtosis, which are not defined. (See Special Floating-Point Values.)

### Syntax

Result = MOMENT( X [, /DOUBLE] [, MDEV=variable] [, /NAN] [, SDEV=variable] )

### Arguments

#### X

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

### Keywords

#### DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

#### MDEV

Set this keyword to a named variable that will contain the mean absolute deviation of X.

#### 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 information on IEEE floating-point values.)

#### SDEV

Set this keyword to a named variable that will contain the standard deviation of X.

### Examples

```; Define an n-element sample population:
X = [65, 63, 67, 64, 68, 62, 70, 66, 68, 67, 69, 71, 66, 65, 70]
; Compute the mean, variance, skewness and kurtosis:
result = MOMENT(X)
PRINT, 'Mean: ', result[0] & PRINT, 'Variance: ', result[1] & \$
PRINT, 'Skewness: ', result[2] & PRINT, 'Kurtosis: ', result[3]
```

IDL prints:

```Mean:       66.7333
Variance:    7.06667
Skewness:   -0.0942851
Kurtosis:   -1.18258
```

Introduced: 4.0