A refinement of normal approximation to Poisson binomial
Let X1,X2,…,Xn be independent Bernoulli random variables with P(Xj=1)=1−P(Xj=0)=pj and let Sn:=X1+X2+⋯+Xn. Sn 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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.717 |
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| Summary: | Let X1,X2,…,Xn be independent Bernoulli random variables with P(Xj=1)=1−P(Xj=0)=pj and let Sn:=X1+X2+⋯+Xn. Sn 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 p1=p2=⋯=pn. |
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| ISSN: | 0161-1712 1687-0425 |