ⓘ Combinant
In the mathematical theory of probability, the combinants c n of a random variable X are defined via the combinantgenerating function G, which is defined from the moment generating function M as
G X t = M X log 1 + t) {\displaystyle G_{X}t=M_{X}\log1+t)}which can be expressed directly in terms of a random variable X as
G X t:= E,\quad t\in \mathbb {R},}wherever this expectation exists.
The n th combinant can be obtained as the n th derivatives of the logarithm of combinant generating function evaluated at –1 divided by n factorial:
c n = 1 n! ∂ n ∂ t n log G t)  t = − 1 {\displaystyle c_{n}={\frac {1}{n!}}{\frac {\partial ^{n}}{\partial t^{n}}}\logGt){\bigg }_{t=1}}Important features in common with the cumulants are:
 the combinants share the additivity property of the cumulants;
 for infinite divisibility probability distributions, both sets of moments are strictly positive.
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 deviation skewness kurtosis L  moment moment  generating function mgf characteristic function probability  generating function pgf cumulant combinant
 deviation skewness kurtosis L  moment moment  generating function mgf characteristic function probability  generating function pgf cumulant combinant
 deviation skewness kurtosis L  moment moment  generating function mgf characteristic function probability  generating function pgf cumulant combinant
Bhatia–Davis inequality 
Cokurtosis 
Comonotonicity 
Concomitant (statistics) 
Conditional probability distribution 
Convolution of probability distributions 
Coskewness 
Hellinger distance 
Infinite divisibility (probability) 
Joint probability distribution 
Khmaladze transformation 
Marginal distribution 
Memorylessness 
Mills ratio 
Neutral vector 
Normalizing constant 
Normally distributed and uncorrelated .. 
Pairwise independence 
Popovicius inequality on variances 
Probability integral transform 
Relationships among probability distr .. 
Shape of a probability distribution 
Smoothness (probability theory) 
Stability (probability) 
Tail dependence 
Truncated distribution 
Truncation (statistics) 
Zero bias transform 
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