A note on Poisson approximation in multivariate case
Cheng-Gee Liu · Kodai Mathematical Journal · 1987
It has been studied in recent years to show the Poisson approximation for the sum of independent Bernoulli random variables which may or may not be identically distributed (see [1], [2], [4]).In paper [3], K. Kawamura has derived sufficient conditions of a Poisson approximation for the sum of independent identically multivariate Bernoulli random variables.In this paper, we are going to extend the result of paper [2] and generalize the result of paper [3] to the multivariate case. Notations and Definitions.a. Suffix and n-dimensional vectors.1. j, k, m, n: positive integers, 2. λ t : parameter of Poisson distribution for every 3. e lf e 2 , -" , e n : base of n-dimensional vectors, 4. E={0,l} n -{O] and EO={0,l} n , 5. O: n-dimensional zero vector.6. i=(z'i, h,for all i€=EO, where 2. Pj(i): P k j{ϊ) expressed in the notation b. 1. will be replaced by P 3 (ϊ) for simplicity if we don't need any information about fixed k,