Gap-free compositions and gap-free samples of geometric random variables
نویسندگان
چکیده
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.
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...
متن کاملGap-Free Samples of Geometric Random Variables
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.
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This paper continues the study of gaps in sequences of geometrically distributed random variables, as started by Hitczenko and Knopfmacher [9], who concentrated on sequences which were gap-free. Now we allow gaps, and count some related parameters. Our notation of gaps just means empty “urns” (within the range of occupied urns). This might be called weak gaps, as opposed to maximal gaps, as in ...
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Motivated by applications in enumerative combinatorics and the analysis of algorithms we investigate the number of gaps and the length of the longest gap in a discrete random sample from a general distribution. We obtain necessary and sufficient conditions on the underlying distribution for the gaps to vanish asymptotically (with probability 1, or in probability), and we study the limiting dist...
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عنوان ژورنال:
- Discrete Mathematics
دوره 294 شماره
صفحات -
تاریخ انتشار 2005