Faculty of Economics and Business Administration Publications Database

A Note on LeCam’s Bound for the Distance Between the Poisson Binomial and the Poisson Distribution

Volume: 43
Number: 3
Pages: 445 - 452
Month: July
Link External Source: Online Version
Year: 2002
Keywords: Poisson binomial distribution; Poisson approximation; Total variation distance

A Poisson binomial distribution with n possibly different success probabilities p1, p2,...,pn is frequently approximated by a Poisson distribution with parameter λ = p1 + p2 + ... + pn. LeCam’s bound p21 + p22 + ... + p2n for the total variation distance between both distributions is particularly useful provided the success probabilities are small.

The paper presents an improved version of LeCam’s bound if a generalized d-dimensional Poisson binomial distribution is to be approximated by a compound Poisson distribution.