Decomposable Statistics Generated by Multidimensional Pólya Distribution

Abstract

Exact and asymptotic formulas for the mathematical expectation and variance for decomposable statistics generated by multidimensional Pólya random walks (with stopping border G: N m=1 k m = = n) are proposed, as well as factorization for the double generating function of these statistics. Scenarios are described when decomposable statistics in the scheme of multidimensional Pólya random walks are asymptotically normal (integral and local normal limit theorems are presented). Also, minimal (natural) constraints are stipulated on the parameter α of the Pólya random walk.