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Article overview
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A study of counts of Bernoulli strings via conditional Poisson processes | Fred W. Huffer
; Jayaram Sethuraman
; Sunder Sethuraman
; | Date: |
14 Jan 2008 | Abstract: | We say that a string of length $d$ occurs, in a Bernoulli sequence, if a
success is followed by exactly $(d-1)$ failures before the next success. The
counts of such $d$-strings are of interest, and in specific independent
Bernoulli sequences are known to correspond to asymptotic $d$-cycle counts in
random permutations.
In this note, we give a new framework, in terms of conditional Poisson
processes, which allows for a quick characterization of the joint distribution
of the counts of all $d$-strings, in a general class of Bernoulli sequences, as
certain mixtures of the product of Poisson measures. This general class
includes all Bernoulli sequences considered before, as well many new sequences. | Source: | arXiv, 0801.2115 | Services: | Forum | Review | PDF | Favorites |
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