 #jsDisabledContent { display:none; } My Account |  Register |  Help Flag as Inappropriate This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate?          Excessive Violence          Sexual Content          Political / Social Email this Article Email Address:

# Combinant

Article Id: WHEBN0041353970
Reproduction Date:

 Title: Combinant Author: World Heritage Encyclopedia Language: English Subject: Collection: Theory of Probability Distributions Publisher: World Heritage Encyclopedia Publication Date:

### Combinant

In the mathematical theory of probability, the combinants cn of a random variableX are defined via the combinant-generating function G(t), which is defined from the moment generating function M(z) as

G_X(t)=M_X(\log(1+t))

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

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:

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:

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.