Statistics Toolbox™

moment - Central moments

Syntax

m = moment(X,order)
moment(X,order,dim)

Description

m = moment(X,order) returns the central sample moment of X specified by the positive integer order. For vectors, moment(x,order) returns the central moment of the specified order for the elements of x. For matrices, moment(X,order) returns central moment of the specified order for each column. For N-dimensional arrays, moment operates along the first nonsingleton dimension of X.

moment(X,order,dim) takes the moment along dimension dim of X.

Remarks

Note that the central first moment is zero, and the second central moment is the variance computed using a divisor of n rather than n – 1, where n is the length of the vector x or the number of rows in the matrix X.

The central moment of order k of a distribution is defined as

where E(x) is the expected value of x.

Example

X = randn([6 5])
X =
  1.1650  0.0591  1.2460 -1.2704 -0.0562
  0.6268  1.7971 -0.6390  0.9846  0.5135
  0.0751  0.2641  0.5774 -0.0449  0.3967
  0.3516  0.8717 -0.3600 -0.7989  0.7562
 -0.6965 -1.4462 -0.1356 -0.7652  0.4005
  1.6961 -0.7012 -1.3493  0.8617 -1.3414

m = moment(X,3)
m =
  -0.0282  0.0571  0.1253  0.1460  -0.4486

See Also

kurtosis, mean, skewness, std, var

mode

multcompare