Abstract
We consider sampling with replacement of equiprobable groups of a fixed size m from a finite population S. Given a subset A ⊂ S, the distributions of (a) the number of distinct elements of A in a sample of size k and (b) the sample size necessary to obtain at least say n elements of A are given. Neat formulas are given especially for the expected values of these, as well as of some related random variables. Further we derive an optimal strategy to collect all elements of S under the assumptions that sampling one group costs α monetary units and that it is possible to purchase the elements which are missing at the end of the sampling procedure at a price of β > α/m per element.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference51 articles.
1. A note on a class of occupancy problems;Sprott;Amer. Statist.,1969
2. Trembley (1794/95) Recherches sur une question relative au calcul des probabilités. Mém. Acad. Berlin , 69–108.
3. Asymptotic Distributions for Occupancy and Waiting Time Problems with Positive Probability of Falling Through the Cells
4. Die Wartezeitverteilung für ein verallgemeinertes Sammlerproblem;Stadje;Did. d. Math.,1989
5. Asymptotic normality in a coupon collector's problem
Cited by
49 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献