Faculty of Economics and Business Administration Publications Database

Bounds for the Total Variation Distance Between the Binomial and the Poisson Distribution in Case of Medium-Sized Success Probabilities

Volume: 36
Number: 1
Pages: 97 - 104
Month: March
Link External Source: Online Version
Year: 1999
Keywords: Binomial distribution; Poisson distribution; Total variation distance; Risk theory; Accumulated claim distribution

In applied probability, the distribution of a sum of n independent Bernoulli random variables with success probabilities p1,p2,…, pn is often approximated by a Poisson distribution with parameter λ = p1 + p2 + pn. Popular bounds for the approximation error are excellent for small values, but less efficient for moderate values of p1,p2,…,pn.

Upper bounds for the total variation distance are established, improving conventional estimates if the success probabilities are of medium size. The results may be applied directly, e.g. to approximation problems in risk theory.