Bounds in poisson approximation for random sums of Bernoulli random variables

Abstract

Let X[subscript n] be a sequence of Bernoulli random variables and a positive integer-valued random variable. Define S[subscript N] = X₁ +X₂ +… X [subscript n]) be random sums. Assume N, X₁, X₂, … are independent. In this thesis, we establish uniform and non-uniform bounds in Poisson approximation for S[subscript N]