A Remainder Term Estimate for the Normal Approximation in Classical Occupancy
Englund, Gunnar
Ann. Probab., Tome 9 (1981) no. 6, p. 684-692 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Let balls be thrown successively at random into $N$ boxes, such that each ball falls into any box with the same probability $1/N$. Let $Z_n$ be the number of occupied boxes (i.e., boxes containing at least one ball) after $n$ throws. It is well known that $Z_n$ is approximately normally distributed under general conditions. We give a remainder term estimate, which is of the correct order of magnitude. In fact we prove that $0.087/\max(3, DZ_n) \leqq \sup_x |P(Z_n < x) - \Phi((x - EZ_n)/DZ_n)| \leqq 10.4/DZ_n.$
Publié le : 1981-08-14
Classification:  Classical occupancy,  normal approximation,  remainder term,  60F05 
@article{1176994376,
     author = {Englund, Gunnar},
     title = {A Remainder Term Estimate for the Normal Approximation in Classical Occupancy},
     journal = {Ann. Probab.},
     volume = {9},
     number = {6},
     year = {1981},
     pages = { 684-692},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176994376}
}

Englund, Gunnar. A Remainder Term Estimate for the Normal Approximation in Classical Occupancy. Ann. Probab., Tome 9 (1981) no. 6, pp.  684-692. http://gdmltest.u-ga.fr/item/1176994376/