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Recursive splitting of an interval when the proportions are identical and independent random variables

Imagine a stick broken at a random point according to the known distribution function F, the right hand piece being discarded. The remaining left hand piece is then broken according to the same (but rescaled) distribution F ad infinitum. What is the largest piece discarded and at what stage of the process does it occur? Using a basic recursive property, these and related questions are studied, in particular when the distribution F is uniform.
Year of publication:
1988
Authors: Lloyd, C. J. ; Williams, E. J.
Published in:
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 28.1988, 1, p. 111-122
Publisher: Elsevier
Keywords: uniform distribution order statistics recurrence relation
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Type of publication: Article
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Persistent link: https://www.econbiz.de/10008872979
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