Gap-Free Samples of Geometric Random Variables
نویسندگان
چکیده
We study the probability that a sample of independent, identically distributed random variables with a geometric distribution is gap-free, that is, that the sizes of the variables in the sample form an interval. We indicate that this problem is closely related to the asymptotic probability that a random composition of an integer n is likewise gap-free.
منابع مشابه
Gaps in samples of geometric random variables
In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225–239] and continued in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈http://www.ulb.ac.be...
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We study the asymptotic probability that a random composition of an integer n is gap-free, that is, that the sizes of parts in the composition form an interval. We show that this problem is closely related to the study of the probability that a sample of independent, identically distributed random variables with a geometric distribution is likewise gap-free.
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