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Recurrence of extreme observations*

Published online by Cambridge University Press:  09 April 2009

S. S. Wilks
S. S. Wilks
Affiliation:
Princeton University.
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Suppose a preliminary set of m independent observations are drawn from a population in which a random variable x has a continuous but unknown cumulative distribution function F(x). Let y be the largest observation in this preliminary sample. Now suppose further observations are drawn one at a time from this population until an observation exceeding y is obtained. Let n be the number of further drawings required to achieve this objective. The problem is to determine the distribution function of the random variable n. More generally, suppose y is the r-th from the largest observation in the preliminary sample and let n denote the number of further trials required in order to obtain k observations which exceed y. What is the distribution function of n?

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 1 , Issue 1 , August 1959 , pp. 106 - 112
Copyright
Copyright © Australian Mathematical Society 1959

References

* This problem arose in some research partially supported by the Office of Naval Research.