A three-parameter binomial approximation
Erol A. Peköz, Adrian Röllin, Vydas Čekanavičius, and Michael Shwartz
Source: J. Appl. Probab. Volume 46, Number 4
(2009), 1073-1085.
Abstract
We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution, where the three parameters (the number of trials, the probability of success, and the shift amount) are chosen to match the first three moments of the two distributions. We give a bound on the approximation error in terms of the total variation metric using Stein's method. A numerical study is discussed that shows shifted binomial approximations are typically more accurate than Poisson or standard binomial approximations. The application of the approximation to solving a problem arising in Bayesian hierarchical modeling is also discussed.
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1261670689
Digital Object Identifier: doi:10.1239/jap/1261670689
Mathematical Reviews number (MathSciNet): MR2582707
Zentralblatt MATH identifier: 1187.60010
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