MOMENT

Syntax | Return Value | Arguments | Keywords | Examples | Version History | See Also

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, ..., x_n-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.

Syntax

Result = MOMENT( X [, /DOUBLE] [, MAXMOMENT={1|2|3|4}] [, MDEV=variable] [, /NAN] [, SDEV=variable] )

Return Value

A four-element vector containing the mean, variance, skewness, and kurtosis of the input vector. 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 (Application Programming).)

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.

MAXMOMENT

Set this keyword to one of the following values to limit the number of moments calculated. Moments that are not calculated are replaced by the IEEE value NaN in the result array.

Note
If X only contains one element, the value of the MAXMOMENT keyword is ignored. In this case, MOMENT returns a Mean equal to X, and NaN for all other output values.

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 (Application Programming) 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 

Version History

See Also

KURTOSIS, HISTOGRAM, MAX, MEAN, MEANABSDEV, MEDIAN, MIN, STDDEV, SKEWNESS, VARIANCE