# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.