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Cumulant

In probability theory and statistics, the cumulants κn of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. Any two probability distributions whose moments are identical will have identical cumulants as well, and vice versa.

History, Some properties of the cumulant generating function & Further properties of cumulants

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Overview

Definition

Some basic properties

Cumulants of some discrete probability distributions

Cumulants of some continuous probability distributions

Some properties of the cumulant generating function

Further properties of cumulants

Joint cumulants

Relation to statistical physics

History

Cumulants in generalized settings

Advanced semantic analysis

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Map overview Semantic statistics

Cumulant

Nodes113
Edges112
Triples121
Avg. degree1.98
Density0.017699
Components1

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Cumulant

Top relations

related to history · 15
Cumulant → Anders Hald, Cumulants, Fisher, Fisher's, Harold Hotelling, In, John Wishart, Neyman, Ronald Fisher, Stephen Stigler, The, They, Thiele, Thiele's, Thorvald
related to Cumulants of some discrete probability distributions · 10
Cumulant → All, Bernoulli, Comparing, Every, Introducing, Poisson, Substituting, The, The Bernoulli, The Poisson
related to Alternative definition of the cumulant generating function · 9
Cumulant → Although, An, Both, Cauchy, Lorentzian, Lévy, Maclaurin, Nevertheless, Some
related to Cumulants of a polynomial sequence of binomial type · 8
Cumulant → Bell, Each, Eric Temple Bell, For, In, Out, The, This
related to Free cumulants · 7
Cumulant → If, In, Roland Speicher, The, These, This, Wigner
related to Joint cumulants · 7
Cumulant → As, Maclaurin, Note, Section, The, X1, Xn
related to Relation with mixed moments · 7
Cumulant → Equation, For, The, XY, XYZ, XZ, YZ
related to Bell numbers · 5
Cumulant → All, Bell, In, Poisson, The Bell
related to Some properties of the cumulant generating function · 5
Cumulant → Big, If, Its, The, X-K
is a · 4
Cumulant → determinant of a matrix, expected value, mean, variance

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Important terminology

cumulants displaystyle kappa moments function textstyle generating random mu distribution sum log first variables operatorname left right terms central moment

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cumulantis amean0.90text
Cumulantis aexpected value0.90text
Cumulantis adeterminant of a matrix0.90text
Cumulantis avariance0.90text
the magnetic field or chemical potential μinstance ofOther free energy can be a function of other variables0.80text
Cumulantrelated to A negative resultGiven0.60section
Cumulantrelated to A negative resultThere0.60section
Cumulantrelated to A negative resultThe0.60section
Cumulantrelated to Alternative definition of the cumulant generating functionSome0.60section
Cumulantrelated to Alternative definition of the cumulant generating functionAn0.60section
Cumulantrelated to Alternative definition of the cumulant generating functionAlthough0.60section
Cumulantrelated to Alternative definition of the cumulant generating functionMaclaurin0.60section

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