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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832563600586178560 |
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| author | K. Neammanee |
| author_facet | K. Neammanee |
| author_sort | K. Neammanee |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e46b2ba50b254df99d648e6d17c1b429 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e46b2ba50b254df99d648e6d17c1b4292025-02-03T01:13:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005571772810.1155/IJMMS.2005.717A refinement of normal approximation to Poisson binomialK. Neammanee0Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandLet 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.http://dx.doi.org/10.1155/IJMMS.2005.717 |
| spellingShingle | K. Neammanee A refinement of normal approximation to Poisson binomial International Journal of Mathematics and Mathematical Sciences |
| title | A refinement of normal approximation to Poisson binomial |
| title_full | A refinement of normal approximation to Poisson binomial |
| title_fullStr | A refinement of normal approximation to Poisson binomial |
| title_full_unstemmed | A refinement of normal approximation to Poisson binomial |
| title_short | A refinement of normal approximation to Poisson binomial |
| title_sort | refinement of normal approximation to poisson binomial |
| url | http://dx.doi.org/10.1155/IJMMS.2005.717 |
| work_keys_str_mv | AT kneammanee arefinementofnormalapproximationtopoissonbinomial AT kneammanee refinementofnormalapproximationtopoissonbinomial |