Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Simple Search

Query:
Enter a query and click »Search«...
Format:
Display: entries per page entries
Zbl 1164.60009
Pósfai, Anna
Rates of convergence for normal approximation in incomplete coupon collection.
(English)
[J] Acta Sci. Math. 73, No. 1-2, 333-348 (2007). ISSN 0001-6969

A coupon collector samples with replacement $n$ distinct coupons (each with equal probability $1/n$). Let $m_n\in \{0, \dots ,n-1\}$. The sampling is repeated until $n-m_n$ distinct coupons are collected for the first time. The waiting time, i.e., the random number of draws until $m_n$ coupons are obtained is denoted by $W_n(m_n)$. Let $\mu_n(m_n)$ and $\sigma^2_n(m_n)$ denote mean and variance of $W_n(m_n)$ and let $F_{n,m_n}$ denote the distribution function of the normalized random variable $(W_n(m_n) -\mu_n(m_n))/\sigma_n(m_n)$. \par First limit theorems (for $n\to\infty)$ had been proved by {\it P. Erdös} and {\it A. Rényi} [Publ. Math. Inst. Hung. Acad. Sci., Ser. A 6, 215--220 (1961; Zbl 0102.35201)] (for $m_n=0$) and by {\it L. E. Baum} and {\it P. Billingsley} [Ann. Math. Stat. 36 1835--1839 (1965; Zbl 0227.62010)] (for $m_n = n$). In the second paper, it was also shown that $\left\{ F_{n.m_n}\right\}$ is asymptotically normal. \par In the paper under review, the author obtains rates of convergence for the asymptotic if $m_n$ and $\left(n-m_n\right)/\sqrt{n}$ tend to $\infty$.
[Wilfried Hazod (Dortmund)]
MSC 2000:
*60F05 Weak limit theorems

Keywords: normal approximation; sampling with replacement

Citations: Zbl 0227.62010; Zbl 0102.35201

Login Username: Password:

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster