Combinant
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
- Kittel, W.; De Wolf, E. A. Soft Multihadron Dynamics. pp. 306 ff. ISBN 978-9812562951. Google Books
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Theory of probability distributions
- probability mass function (pmf)
- probability density function (pdf)
- cumulative distribution function (cdf)
- quantile function
![](http://upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Loglogisticpdf_no-labels.svg/90px-Loglogisticpdf_no-labels.svg.png)
- raw moment
- central moment
- mean
- variance
- standard deviation
- skewness
- kurtosis
- L-moment
- moment-generating function (mgf)
- characteristic function
- probability-generating function (pgf)
- cumulant
- combinant
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