VoseRawMoments

See also: VoseRawMoment1, VoseRawMoment2, VoseRawMoment3, VoseRawMoment4, VoseMoments

VoseRawMoments(Distribution)

 

 

 

Array function that returns the first four raw moments of a distribution.

The output array should be either 4x1 or 1x4 in which case the values of the raw moments will be returned, or 4x2 or 2x4 in which case labels will be included.

The raw moments (or 'moments about zero') of a distribution  are defined as

,

for continuous distributions with PDF f(x) and

for discrete distributions with PMF pi.

The central moments (or 'moments about the mean') for are defined as:

with analogue definitions for discrete variables. The lower central moments are directly related to the variance, skewness and kurtosis. The second, third and fourth central moments can be expressed in terms of the raw moments as follows:

 

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