| 31. | A cumulant generating function ( CGF ) may then be obtained from the cumulant function.
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| 32. | It can be characterized by its moment generating function:
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| 33. | However, the moment generating function exists only for distributions that have a defined Laplace transform.
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| 34. | Then the "'Whitney rank generating function "'is defined as
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| 35. | In consequence the moment generating function is not defined.
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| 36. | G _ a ( z ) is called the generating function of the sequence a.
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| 37. | Replacing by gives the moment generating function of.
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| 38. | The Taylor series using the moments as they usually occur in the moment generating function yields
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| 39. | The Cauchy distribution has no moment generating function.
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| 40. | Often the manipulation of integrals can be avoided by use of some type of generating function.
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