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, ..., 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.

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 

Version History

Introduced: 4.0

See Also

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