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Extremal processes and random measures

Published online by Cambridge University Press:  14 July 2016

R. W. Shorrock
R. W. Shorrock*
Affiliation:
Université de Montréal
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Abstract

Discrete time extremal processes with a continuous underlying c.d.f. are random measures which can be viewed as two-dimensional Poisson processes and this representation is used to obtain the conditional law of the sequence of states the process passes through (upper record values) given the sequence of holding times in states (inter-record times). In addition the Gamma processes (which lead to the Ferguson Dirichlet processes) and a random measure that arises in sampling from a biological population are discussed as two-dimensional Poisson processes.

Keywords

POISSONGAMMADIRICHLETBIOLOGICAL POPULATIONPOINT PROCESSFORMAL BAYES
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 316 - 323
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Anscombe, F. J. (1950) Sampling theory of the negative binomial and logarithmic series distribution. Biometrika 37, 358–382.CrossRefGoogle Scholar
[2] Dwass, M. (1973) Extremal processes III, Discussion Paper No. 41, The Center for Mathematical Studies in Economics and Management Sciences, Northwestern University.Google Scholar
[3] Ferguson, T. (1973) A Bayesian analysis of some non-parametric problems. Ann. Statist. 1, 209–230.Google Scholar
[4] Fisher, R. A., Corbet, A. S. and Williams, C. B. (1943) The relation between the number of species and the number of individuals in a random sample of an animal population. J. Animal Ecology 12, 42–58.Google Scholar
[5] Kendall, D.G. (1948) On some modes of population growth leading to Fisher's logarithmic series distribution. Biometrika 35, 6–15.Google Scholar
[6] Kendall, M. G. and Stuart, A. (1963) The Advanced Theory of Statistics Vol. I. Charles Griffin and Company, London.Google Scholar
[7] Resnick, S. (1974) Inverses of extremal processes. Adv. Appl. Prob. 6, 392–406.Google Scholar
[8] Shorrock, R. (1972) A limit theorem for inter-record times. J. Appl. Prob. 9, 219–223.Google Scholar
[9] Shorrock, R. (1973) Record values and inter-record times. J. Appl. Prob. 10, 543–555.Google Scholar
[10] Shorrock, R. (1974) On discrete time extremal processes. Adv. Appl. Prob. 6, 580–592.Google Scholar