Margaret Archibald ; Arnold Knopfmacher - Samples of geometric random variables with multiplicity constraints

dmtcs:3490 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities - https://doi.org/10.46298/dmtcs.3490
Samples of geometric random variables with multiplicity constraintsArticle

Authors: Margaret Archibald 1; Arnold Knopfmacher 1

  • 1 The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]

We investigate the probability that a sample $\Gamma=(\Gamma_1,\Gamma_2,\ldots,\Gamma_n)$ of independent, identically distributed random variables with a geometric distribution has no elements occurring exactly $j$ times, where $j$ belongs to a specified finite $\textit{'forbidden set'}$ $A$ of multiplicities. Specific choices of the set $A$ enable one to determine the asymptotic probabilities that such a sample has no variable occuring with multiplicity $b$, or which has all multiplicities greater than $b$, for any fixed integer $b \geq 1$.


Volume: DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
Section: Proceedings
Published on: January 1, 2006
Imported on: May 10, 2017
Keywords: Geometric random variable,Mellin transform,Poisson transform,multiplicity,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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