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.
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.)
Result = MOMENT( X [, /DOUBLE] [, MDEV=variable] [, /NAN] [, SDEV=variable] )
An n-element integer, single-, or double-precision floating-point vector.
Set this keyword to force the computation to be done in double-precision arithmetic.
Set this keyword to a named variable that will contain the mean absolute deviation of X.
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.)
Set this keyword to a named variable that will contain the standard deviation of X.
; 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 & PRINT, 'Variance: ', result & $ PRINT, 'Skewness: ', result & PRINT, 'Kurtosis: ', result
Mean: 66.7333 Variance: 7.06667 Skewness: -0.0942851 Kurtosis: -1.18258
KURTOSIS, HISTOGRAM, MAX, MEAN, MEANABSDEV, MEDIAN, MIN, MOMENT, STDDEV, SKEWNESS, VARIANCE