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| In the mathematical theory of probability, the '''combinants''' ''c''<sub>''n''</sub> 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
| | Physiotherapist Broadbent from Kuujjuaq, has several hobbies and interests that include butterflies, [http://lunspace.com/?option=com_k2&view=itemlist&task=user&id=20421 top 20 property developers in singapore] developers in singapore and cloud watching. Recently has traveled to Chan Chan Archaeological Zone. |
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| :<math>G_X(t)=M_X(\log(1+t))</math>
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| which can be expressed directly in terms of a [[random variable]] ''X'' as
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| :<math> G_X(t) := E\left[(1+t)^X\right], \quad t \in \mathbb{R}, </math>
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| wherever this [[expected value|expectation]] exists.
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| The ''n''th combinant can be obtained as the ''n''th derivatives of the logarithm of combinant generating function evaluated at –1 divided by ''n'' factorial:
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| :<math> c_n = \frac{1}{n!} \frac{\partial ^n}{\partial t^n} \log(G (t)) \bigg|_{t=-1} </math>
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| Important features in common with the [[cumulant]]s are:
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| * the combinants share the additivity property of the cumulants;
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| * for [[infinite divisibility (probability)]] distributions, both sets of moments are strictly positive.
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| ==References==
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| * {{cite book |last1=Kittel|first1=W. |last2=De Wolf |first2=E. A. |title=Soft Multihadron Dynamics |isbn=978-9812562951 |pages=306 ff}} [http://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]
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| {{Theory of probability distributions}}
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| [[Category:Theory of probability distributions]]
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Latest revision as of 06:33, 1 December 2014
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