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BUILT-IN MATHEMATICA SYMBOL
CentralMomentGeneratingFunction
CentralMomentGeneratingFunction[dist, t]
gives the central moment-generating function for the symbolic distribution dist as a function of the variable t.
CentralMomentGeneratingFunction[dist, {t1, t2, ...}]
gives the central moment-generating function for the multivariate symbolic distribution dist as a function of the variables 
, 
, ....
Details
- CentralMomentGeneratingFunction[dist, t] is given by Expectation[Exp[t(x-
)], x
dist] where =Mean[dist]. - CentralMomentGeneratingFunction[dist, {t1, t2, ...}] is equivalent to Expectation[Exp[t.(x-)], xdist] for vectors t and x and where =Mean[dist].
- The i
central moment can be extracted from a central moment-generating function cmgf through SeriesCoefficient[cmgf, {t, 0, i}]i!.
New in 8
