MOMENT

The MOMENT function computes the mean, variance, skewness, and kurtosis of a sample population contained in an n -element vector X . If the vector contains n identical elements, MOMENT computes the mean and variance, and returns the IEEE value NaN for the skewness 5and kurtosis, which are not defined. (See Special Floating-Point Values .)

When x = ( x ₀ , x ₁ , x ₂ , ..., 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.

Calling Sequence

Result = MOMENT( X )

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 value NaN in the input data. Elements with the value NaN are treated as missing data. (See Special Floating-Point Values for more information on IEEE floating-point values.)

SDEV

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

Example

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