| 31. | The geometric stable characteristic function can be expressed in terms of a stable characteristic function as:
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| 32. | Specifically, a game is " convex " if its characteristic function v is supermodular:
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| 33. | :Even better is to have a look at the article Characteristic function ( probability theory ).
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| 34. | Using the characteristic function representation for the wrapped normal distribution in the left side of the integral:
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| 35. | The characteristic function representation for the wrapped Cauchy distribution in the left side of the integral is:
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| 36. | But a geometric stable distribution can be defined by its characteristic function, which has the form:
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| 37. | In other words, the probability is obtained by integrating the characteristic function of against the countably additive measure
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| 38. | The right hand side equals the characteristic function of a standard normal distribution, which implies through sample average
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| 39. | A random variable " X " is called stable if its characteristic function can be written as
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| 40. | There is also a relationship between the stable distribution characteristic function and the geometric stable distribution characteristic function.
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