On gaps and unoccupied urns in sequences of geometrically distributed random variables
نویسندگان
چکیده
منابع مشابه
The number of gaps in sequences of geometrically distributed random variables
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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We study d–records in sequences generated by independent geometric random variables and derive explicit and asymptotic formulæ for expectation and variance. Informally speaking, a d–record occurs, when one computes the d–largest values, and the variable maintaining it changes its value while the sequence is scanned from left to right. This is done for the “strict model,” but a “weak model” is a...
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Run statistics about a sequence of independent geometrically distributed random variables has attracted some attention recently in many areas such as applied probability, reliability, statistical process control, and computer science. In this paper, we first study the mean and variance of the number of alternating runs in a sequence of independent geometrically distributed random variables. The...
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We consider a sequence of n geometric random variables and interpret the outcome as an urn model. For a given parameter m, we treat several parameters like what is the largest urn containing at least (or exactly) m balls, or how many urns contain at least m balls, etc. Many of these questions have their origin in some computer science problems. Identifying the underlying distributions as (varia...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.04.012