| 1. | Two random variables having equal moment generating functions have the same distribution.
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| 2. | All higher characteristic function and moment generating function are both equal to one.
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| 3. | In consequence the moment generating function is not defined.
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| 4. | It can be characterized by its moment generating function:
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| 5. | The Cauchy distribution has no moment generating function.
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| 6. | Replacing by gives the moment generating function of.
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| 7. | The Taylor series using the moments as they usually occur in the moment generating function yields
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| 8. | However, the moment generating function exists only for distributions that have a defined Laplace transform.
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| 9. | The moment generating functions are derived and skewness and kurtosis are obtained from MGF by Muraleedharan and Guedes Soares
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| 10. | Basic AJDs are attractive for modeling default times in credit risk applications, since both the moment generating function
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