A refinement of normal approximation to Poisson binomial

K. Neammanee

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-12

Abstract:

Let X 1 , X 2 , … , X n be independent Bernoulli random variables with P ( X j = 1 ) = 1 − P ( X j = 0 ) = p j and let S n : = X 1 + X 2 + ⋯ + X n . S n is called a Poisson binomial random variable and it is well known that the distribution of a Poisson binomial random variable can be approximated by the standard normal distribution. In this paper, we use Taylor's formula to improve the approximation by adding some correction terms. Our result is better than before and is of order 1 / n in the case p 1 = p 2 = ⋯ = p n .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:679348

DOI: 10.1155/IJMMS.2005.717

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