“Combinant”的意思、由来-开放百科全书

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Combinant

释义

References

In the mathematical theory of probability, the combinants c_n of a random variableX 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

{{cite book |last1=Kittel|first1=W. |last2=De Wolf |first2=E. A. |title=Soft Multihadron Dynamics |isbn=978-9812562951 |pages=306 ff}} [https://books.google.com/books?id=BiEo3IIn4JAC&pg=PA307&lpg=PA307&dq=cumulants+combinants&source=bl&ots=gJyq7LUekt&sig=IOdcKmmEkOL6DCKUnrwVmrImj7s&hl=en&sa=X&ei=dLCnUuOYCsrwoASjk4CoCA&ved=0CFgQ6AEwBA#v=onepage&q=cumulants%20combinants&f=false Google Books]

1 : Theory of probability distributions

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