zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Poisson approximation in a Poisson limit theorem inspired by coupon collecting. (English) Zbl 1173.60008

This paper is concerned with a Poisson approximation for the distribution of sums of asymptotically negligible integer-valued random variables in the setting of row-wise independent triangular arrays. The author refines the classical Poisson convergence theorem of B. V. Gnedenko and A. N. Kolmogorov [Limit distributions for sums of independent random variables. Translated from the Russian by K. L. Chung. Cambridge: Addison-Wesley Publishing Company (1954; Zbl 0056.36001)]. The upper and lower error bounds are expressed in terms of the total variation distance.

The results are applied to the case of the coupon collector’s problem when the distribution of the collector’s waiting time is asymptotically Poisson.

60F05Central limit and other weak theorems
62E17Approximations to statistical distributions (nonasymptotic)
62E20Asymptotic distribution theory in statistics