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
which can be expressed directly in terms of a random variable X as
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:
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.
References
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