A WAITING TIME DISTRIBUTION ARISING FROM THE COUPON COLLECTOR'S PROBLEM.

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Abstract:

A certain waiting time distribution is considered which arises in the context of the Coupon Collectors Problem. In general, the term Coupon Collectors Problem refers to the problem which confronts an individual who is attempting to collect a subset of some set of distinct items, by sampling with replacement, one item from this set on each of a sequence of independent trials, until this subset is obtained. The waiting time in question, denoted by Sr,N N 1,2,... r 1,2,...,N, is the number of trials needed to obtain for the first time, r distinct elements from among N distinct elements, if each of the sequence of independent trials consists of sampling with replacement and equal probabilities, one element from among the N. The exact distribution of Sr,N is obtained. Using this result an asymptotic approximation to this distribution is derived for the case r N. Calculations illustrating the effectiveness of this approximation in the case N 1000, are given. Author

Author(s):
Rubin, Herman ; Zidek, James
Author Organization(s):
STANFORD UNIV CALIF DEPT OF STATISTICS
Descriptive Note:
Technical rept.,
Annotation:
Waiting time distribution arising from the coupon collector's problem.
Pagination:
0012

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
TR-107
Contract/Grant Number(s):
Nonr22552
Project Number(s):
NR342 022
 Subject Terms
Communities of Interest:
No COI(s) Identified
Descriptor(s):
(*SAMPLING, DISTRIBUTION THEORY), PROBABILITY, SEQUENCES(MATHEMATICS), GAME THEORY
Report Date:
1965 Aug 05