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