On pointwise binomial approximation for independent beta binomial random variables

摘要

Stein's method and the beta binomial w-functions are used to derivea non-uniform bound for the point metric between the distribution ofa sum of n independent beta binomial random variables, each withparameters ni; i and i, and a binomial distribution with parametersm =Pni=1 ni and p = 1mPni=1ni i i+ i. The bound is an appropriatemeasurement when all i are large, with respect to all ni and i.