The limit behavior of an interval splitting scheme

We split [0,1] in a uniform manner, take the largest of the two intervals thus obtained, split this interval again uniformly, and continue in this fashion ad infinitum. We show that the extremes of this interval converge almost surely to a beta (2,2) random variable.

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Year of publication:	1986
Authors:	Devroye, Luc ; Letac, Gerard ; Seshadri, Vanamamalai
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 4.1986, 4, p. 183-186
Publisher:	Elsevier
Keywords:	spacings uniform distribution random processes strong convergence beta distribution limit laws

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005137723