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Symmetric sampling procedures, general epidemic processes and their threshold limit theorems

Published online by Cambridge University Press:  14 July 2016

Anders Martin-Löf
Anders Martin-Löf*
Affiliation:
The Folksam Group
*
∗Postal address: The Folksam Group, Box 20500, S-104 60 Stockholm, Sweden.
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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.

Keywords

ITERATIVE SAMPLING PROCEDURESCHAIN LETTERSFACTORIAL SERIES DISTRIBUTIONS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 265 - 282
Copyright
Copyright © Applied Probability Trust 1986 

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References

[1] Von Bahr, B. and Martin-Löf, A. (1980) Threshold limit theorems for some epidemic processes. Adv. Appl. Prob. 12, 319–349.Google Scholar
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