Convergence to a Stable Distribution Via Order Statistics

摘要: Let $X_1, X_2, \cdots$ be i.i.d. random variables whose common distribution function $F$ is in the domain of attraction a nonnormal stable distribution. A simple, probabilistic proof convergence normalized partial sums to given. The makes use an elementary property order statistics and clarifies manner which largest few summands determine limiting method applied self-norming deduce representation for affords explanation infinite discontinuities densities occur some cases. Application technique prove weak separable Hilbert space explored.