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On the Rate of Multivariate Poisson Convergence

✍ Scribed by Bero Roos

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 141 KB
Volume: 69
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1998.1789

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✦ Synopsis

The distribution of the sum of independent nonidentically distributed Bernoulli random vectors in R k is approximated by a multivariate Poisson distribution. By using a multivariate adaption of Kerstan's (1964, Z. Wahrsch. verw. Gebiete 2, 173 179) method, we prove a conjecture of Barbour (1988, J. Appl. Probab. 25A, 175 184) on removing a log-term in the upper bound of the total variation distance. Second-order approximations are included.

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