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The A.S. Limit Distribution of the Longest Head Run

Published online by Cambridge University Press:  20 November 2018

Tamás F. Móri
Tamás F. Móri*
Affiliation:
Department of Probability Theory and Statistics Eotvos Lor and University H-J088 Budapest Hungary
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Abstract

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It is well known that the length Zn of the longest head run observed in n tosses with a fair coin is approximately equal to log2n with a stochastically bounded remainder term. Though — log2n does not converge in law, in the present paper it is shown to have almost sure limit distribution in the sense of the a. s. central limit theorem having been studied recently. The results are formulated and proved in a general setup covering other interesting problems connected with patterns and runs such as the longest monotone block or the longest tube of a random walk.

Keywords

60C0560F15runspatternswaiting timesalmost sure central limit theorem
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 6 , 01 December 1993 , pp. 1245 - 1262
Copyright
Copyright © Canadian Mathematical Society 1993

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