This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# FactorialMoment

 FactorialMoment gives the r moment of the elements in the list. FactorialMomentgives the r moment of the symbolic distribution dist. FactorialMoment[r]represents the r factorial moment.
• For the list , the factorial moment is given by .
Compute factorial moment from data:
Use symbolic data:
Compute the second factorial moment of a discrete univariate distribution:
The second factorial moment of a continuous univariate distribution:
The factorial moment for a multivariate distribution:
Find relation of formal factorial moment to raw moments:
Evaluate for a particular distribution:
Compute factorial moment from data:
 Out[1]=
Use symbolic data:
 Out[2]=
 Out[3]=

Compute the second factorial moment of a discrete univariate distribution:
 Out[1]=

The second factorial moment of a continuous univariate distribution:
 Out[1]=

The factorial moment for a multivariate distribution:
 Out[1]=

Find relation of formal factorial moment to raw moments:
 Out[1]=
Evaluate for a particular distribution:
 Out[2]=
 Out[3]=
 Scope   (8)
Compute factorial moment for univariate distributions:
Compute factorial moment of specific order:
Evaluate factorial moment of specific order numerically:
Compute factorial moment for multivariate distributions:
Compute factorial moment of a formula-defined distribution:
Compute factorial moments of distributions derived from data:
Compute factorial moment for a set of 5 i.i.d. samples of size 1000:
 Applications   (2)
Estimate parameters of a distribution using the method of moments:
Compare data and the estimated parametric distribution:
Reconstruct probability mass function from the sequence of factorial moments:
Find the factorial moment generating function (fmgf):
Use equivalence of the fmgf and the probability generating function:
Verify that factorial moments of the found distribution match the originals:
Factorial moment is equivalent to an expectation of FactorialPower:
First factorial moment is equivalent to Mean:
FactorialMoment can be computed from Moment through :
MomentConvert produces the same result:
Moment can be computed from FactorialMoment through :
MomentConvert produces the same result:
New in 8