Cumulant

Cumulant[dist,r]

gives the r cumulant of the distribution dist.

Cumulant[list,r]

gives the r cumulant of the elements in the list.

Cumulant[r]

represents the r formal cumulant.

Details • For a distribution dist, the r cumulant is given by the coefficient of in CumulantGeneratingFunction[dist,t].
• For a multivariate distribution dist, the {r1,r2,} cumulant is given by the series coefficient of in CumulantGeneratingFunction[dist,{t1,t2,}].
• Cumulant[list,r] is computed from the equivalent expression of sample moments.
• Cumulant handles both numerical and symbolic data.
• Cumulant works with SparseArray objects.
• Cumulant[r] can be used in such functions as MomentConvert and MomentEvaluate, etc.

Examples

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Basic Examples(2)

Compute cumulants from data:

 In:= In:= Out= Use symbolic data:

 In:= Out= Compute the second cumulant of a continuous univariate distribution:

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

 In:= Out= Neat Examples(2)

Introduced in 2010
(8.0)