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combinants

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There are 10 letters in COMBINANTS ( A1B3C3I1M3N1O1S1T1 )

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Definitions of combinants in various dictionaries:

COMBINANTS - In the mathematical theory of probability, the combinants cn of a random variable X are defined via the combinant-generating function G(t), which is ...

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Combinants might refer to
In the mathematical theory of probability, the Combinants cn of a random variable X are defined via the combinant-generating function G(t), which is defined from the moment generating function M(z) as*
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* {\displaystyle G_{X}(t)=M_{X}(\log(1+t))}
* which can be expressed directly in terms of a random variable X as
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* {\displaystyle G_{X}(t):=E\left[(1+t)^{X}\right],\quad t\in \mathbb {R} ,}
* wherever this expectation exists.
* The nth combinant can be obtained as the nth derivatives of the logarithm of combinant generating function evaluated at –1 divided by n factorial:
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* {\displaystyle c_{n}={\frac {1}{n!}}{\frac {\partial ^{n}}{\partial t^{n}}}\log(G(t)){\bigg |}_{t=-1}}
* Important features in common with the cumulants are:
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* 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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