On Sums of Products of Bernoulli Variables and Random Permutations

Anatole Joffe, Éric Marchand, François Perron () and Paul Popadiuk
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Anatole Joffe: Département de Mathématiques et de Statistique
Éric Marchand: Department of Mathematics and Statistics
François Perron: Département de Mathématiques et de Statistique
Paul Popadiuk: Department of Mathematics and Statistics

Journal of Theoretical Probability, 2004, vol. 17, issue 1, 285-292

Abstract: Abstract Let {X k } k≥1 be independent Bernoulli random variables with parameters p k . We study the distribution of the number or runs of length 2: that is $$S_n = \sum {_{k = 1}^n {\text{ }}X_k X_{k + 1}}$$ . Let S=lim n→∞ S n . For the particular case p k =1/(k+B), B being given, we show that the distribution of S is a Beta mixture of Poisson distributions. When B=0 this is a Poisson(1) distribution. For the particular case p k =p for all k we obtain the generating function of S n and the limiting distribution of S n for $$p = \sqrt {\lambda h} + o(1/\sqrt n )$$ .

Keywords: Random permutations; Poisson distribution; Bernouilli random variables (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTP.0000020485.34082.8c

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