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The condition for an approximation of Poisson distribution to Bernoulli sums in multivariate distribution. (English) Zbl 0661.62038
A problem concerning necessary conditions for the approximation of Poisson distributions by the sum of independent Bernoulli sequences in the multivariate case is discussed. One of the conditions proved by the author is \(N p_ i\to \lambda_ i\) as \(N\to \infty\) for \(i\in E\), where \(E=\{0,1\}^ n-0\), \(0=(0,0,...,0)\).
Reviewer: Su Chun

MSC:
62H10 Multivariate distribution of statistics
62E20 Asymptotic distribution theory in statistics
60F05 Central limit and other weak theorems
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[1] K. KAWAMURA, The structure of multivariate Poisson distribution, Kodai Math. J. 2(3) (1979), 337-345. · Zbl 0434.60019 · doi:10.2996/kmj/1138036064
[2] C. Liu, A note on Poisson approximation in multivariate case, Kodai Math. J. 10(2) (1987), 223-230 · Zbl 0633.60034 · doi:10.2996/kmj/1138037417
[3] A. W. MARSHALL AND I. OLKIN, A family of bivariate distributions generated b thebivariate Bernoulli distribution, Journal of the A. S. A., (June 1985), 332-338. · Zbl 0575.60023 · doi:10.2307/2287890
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