The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 5, Number 1 (1995), 294-309.
How Many IID Samples Does it Take to See all the Balls in a Box?
Abstract
Suppose a box contains $m$ balls, numbered from 1 to $m$. A random number of balls are drawn from the box, their numbers are noted and the balls are then returned to the box. This is done repeatedly, with the sample sizes being iid. Let $X$ be the number of samples needed to see all the balls. This paper uses Markov-chain coupling to derive a simple but typically very accurate approximation for $EX$ in terms of the sample size distribution. The approximation formula generalizes the formula found by Polya for the special case of fixed sample sizes.
Article information
Source
Ann. Appl. Probab., Volume 5, Number 1 (1995), 294-309.
Dates
First available in Project Euclid: 19 April 2007
Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004841
Digital Object Identifier
doi:10.1214/aoap/1177004841
Mathematical Reviews number (MathSciNet)
MR1325054
Zentralblatt MATH identifier
0823.60054
JSTOR
links.jstor.org
Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Keywords
Coupon collector's problem Markov chains Markov-chain coupling
Citation
Sellke, Thomas M. How Many IID Samples Does it Take to See all the Balls in a Box?. Ann. Appl. Probab. 5 (1995), no. 1, 294--309. doi:10.1214/aoap/1177004841. https://projecteuclid.org/euclid.aoap/1177004841
