Geodesic
On a~Poisson approximation for the distribution of the number of empty cells in a~nonhomogeneous allocation scheme
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 184-189

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A nonhomogeneous polynomial scheme of allocation of particles into cells is considered in which different allocation laws of particles are allowed. Explicit estimates are given for the accuracy of the Poisson approximation of the distribution of the number of empty cells in an arbitrary subset of cells. The proof of the main theorem uses the combination of the Chen–Stein method with the common probability space method described in the monograph [A. D. Barbour, L. Holst, and S. Janson, Poisson Approximation, Oxford University Press, Oxford, 1992].
Keywords: random allocations, nonhomogeneous scheme, the number of empty cells, the Chen–Stein method.
Mots-clés : Poisson approximation 
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     author = {V. G. Mikhailov},
     title = {On {a~Poisson} approximation for the distribution of the number of empty cells in a~nonhomogeneous allocation scheme},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {184--189},
     publisher = {mathdoc},
     volume = {42},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a12/}
}
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V. G. Mikhailov. On a~Poisson approximation for the distribution of the number of empty cells in a~nonhomogeneous allocation scheme. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 184-189. http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a12/