# FactorialMomentGeneratingFunction

gives the factorial moment-generating function for the distribution dist as a function of the variable t.

FactorialMomentGeneratingFunction[dist,{t1,t2,}]

gives the factorial moment-generating function for the multivariate distribution dist as a function of the variables t1, t2, .

# Details • FactorialMomentGeneratingFunction is also known as probability generating function (pgf).
• is equivalent to Expectation[tx,xdist].
• FactorialMomentGeneratingFunction[dist, {t1,t2,}] is equivalent to Expectation[t1x1t2x2,{x1,x2,}dist].
• The i factorial moment can be extracted from a factorial moment-generating function fmgf through SeriesCoefficient[fmgf,{t,1,i}]i!.
• The probability for a discrete random variable to assume the value i can be extracted from a factorial moment-generating function expr through SeriesCoefficient[expr,{t,0,i}].

# Examples

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## Basic Examples(3)

The factorial moment-generating function (fmgf) for a univariate discrete distribution:

 In:= Out= Compute an fmgf for a continuous univariate distribution:

 In:= Out= The fmgf for a multivariate distribution:

 In:= Out= ## Possible Issues(2)

Introduced in 2010
(8.0)