On some limit properties for the power series distribution.

This scheme generalizes the classical scheme of allocation of particles to cells (see [[5]]) and hence gets its name. Law of large numbers, local limit theorem, Allocation scheme, power series distribution, almost sure central limit theorem, moderate deviation principle Keywords: Allocation scheme; power series distribution; law of large numbers; almost sure central limit theorem; moderate deviation principle; local limit theorem EN Allocation scheme power series distribution law of large numbers almost sure central limit theorem moderate deviation principle local limit theorem 193 205 13 06/17/22 20220601 NES 220601 Note: Originally published in Diskretnaya Matematika (2022) 34,No1, 88-102 (in Russian). [Extracted from the article]