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Download a pdf copy of this help file here |
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Download a pdf copy of this help file here |
See also: VoseRawMoments, VoseMoments, Method of Moments (MoM)
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:
ModelRisk allows one to directly calculate all four raw moments of a distribution object through the VoseRawMoments function.