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Mathematica > Data Manipulation > Statistical Data Analysis > Probability & Statistics > Statistical Moments and Generating Functions > FactorialMoment >
Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Probability & Statistics > Statistical Moments and Generating Functions > FactorialMoment >
Mathematica > Data Manipulation > Statistical Data Analysis > Probability & Statistics > Statistical Distribution Functions > Statistical Moments and Generating Functions > FactorialMoment >
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FactorialMoment

FactorialMoment
gives the r^(th) moment of the elements in the list.
FactorialMoment
gives the r^(th) moment of the symbolic distribution dist.
FactorialMoment[r]
represents the r^(th) factorial moment.
MORE INFORMATION
  • For the list , the ^(th) factorial moment is given by .
EXAMPLESCLOSE ALL
Basic Examples   (5)
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:
In[1]:=
Click for copyable input
Out[1]=
Use symbolic data:
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
 
Compute the second factorial moment of a discrete univariate distribution:
In[1]:=
Click for copyable input
Out[1]=
 
The second factorial moment of a continuous univariate distribution:
In[1]:=
Click for copyable input
Out[1]=
 
The factorial moment for a multivariate distribution:
In[1]:=
Click for copyable input
Out[1]=
 
Find relation of formal factorial moment to raw moments:
In[1]:=
Click for copyable input
Out[1]=
Evaluate for a particular distribution:
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
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:
TraditionalForm formatting:
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:
Properties & Relations   (4)
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:
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