Accuracy of approximation in the Poisson theorem in terms of the χ2-distance
2008
We study the limit behavior of the χ2-distance between the distributions of the nth partial sum of independent not necessarily identically distributed Bernoulli random variables and the accompanying Poisson law. As a consequence in the i.i.d. case we make the multiplicative constant preciser in the available upper bound for the rate of convergence in the Poisson limit theorem.
Keywords:
- Compound Poisson distribution
- Central limit theorem
- Poisson binomial distribution
- Infinite divisibility (probability)
- Poisson limit theorem
- Mathematical analysis
- Uniqueness theorem for Poisson's equation
- Poisson distribution
- Poisson regression
- Mathematics
- Independent and identically distributed random variables
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