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Distribution of the Time of the First k-Record

Published online by Cambridge University Press:  27 July 2009

Ilan Adler  and
Sheldon M. Ross
Ilan Adler
Affiliation:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720
Sheldon M. Ross
Affiliation:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720
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Abstract

We compute the first two moments and give a recursive formula for the generating function of the first k-record index for a sequence of independent and identically distributed random variables that take on a finite set of possible values. When the random variables have an infinite support, we bound the distribution of the index of the first k-record and show that its mean is infinite.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 3 , July 1997 , pp. 273 - 278
Copyright
Copyright © Cambridge University Press 1997

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References

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