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2 results

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

  • Anders Martin-Löf
  • Journal:
    Journal of Applied Probability / Volume 23 / Issue 2 / June 1986
    Published online by Cambridge University Press:
    14 July 2016, pp. 265-282
    Print publication:
    June 1986

  • 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.

  • Random contact processes, snowball sampling and factorial series distributions

  • Sven Berg
  • Journal:
    Journal of Applied Probability / Volume 20 / Issue 1 / March 1983
    Published online by Cambridge University Press:
    14 July 2016, pp. 31-46
    Print publication:
    March 1983

  • A contact process first posed as a random mapping problem is discussed together with a model for the spread of a rumour through an archaic telephone system. Snowball sampling and the well-known Reed–Frost chain binomial model are also commented on. Our main interest and emphasis is on distributional properties of discrete-time models. Simple combinatorial arguments are used along with a class of discrete distributions originally proposed for catch–recapture sampling.