Abstract
Iterative sampling procedures of a general type in a finite population are considered. They generalize the Reed-Frost process in that binomial sampling is replaced by an arbitrary symmetric sampling defined by a factorial series distribution. Threshold limit theorems are proved saying that the total number of sampled objects is either small with a certain limit distribution, or a finite fraction of the population with a Gaussian limit distribution as the size of the population gets large. These results extend earlier ones for the Reed-Frost process [1], and are proved in a more direct way than before.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference7 articles.
1. Limit theorems for sequences of jump Markov processes approximating ordinary differential processes
2. Random contact processes, snowball sampling and factorial series distributions
3. Factorial series distributions, with applications to capture-recapture problems;Berg;Scand. J. Statist.,1980
4. On the maximum of a branching process;Lindvall;Scand. J. Statist.,1976
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