A Pólya Approximation to the Poisson-Binomial Law
Author:
- 1 June 2012
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 49 (03) , 745-757
Abstract
Using Stein's method, we derive explicit upper bounds on the total variation distance between a Poisson-binomial law (the distribution of a sum of independent but not necessarily identically distributed Bernoulli random variables) and a Pólya distribution with the same support, mean, and variance; a nonuniform bound on the pointwise distance between the probability mass functions is also given. A numerical comparison of alternative distributional approximations on a somewhat representative collection of case studies is also exhibited. The evidence proves that no single one is uniformly most accurate, though it suggests that the Pólya approximation might be preferred in several parameter domains encountered in practice.Keywords
This publication has 21 references indexed in Scilit:
- Polynomial Birth–Death Distribution Approximation in the Wasserstein DistanceJournal of Theoretical Probability, 2009
- Stein’s method for discrete Gibbs measuresThe Annals of Applied Probability, 2008
- A polynomial birth–death point process approximation to the Bernoulli processStochastic Processes and their Applications, 2008
- Exchangeable pairs and Poisson approximationProbability Surveys, 2005
- Approximating the number of successes in independent trials: Binomial versus PoissonThe Annals of Applied Probability, 2002
- Almost-Binomial Random VariablesThe College Mathematics Journal, 2002
- Stein's Method and Birth-Death ProcessesThe Annals of Probability, 2001
- Asymptotic Expansions in the Exponent: a Compound Poisson ApproachAdvances in Applied Probability, 1997
- Binomial approximation to the Poisson binomial distributionStatistics & Probability Letters, 1991
- Chromatic polynomials and logarithmic concavityJournal of Combinatorial Theory, Series B, 1974