The Number of Two Consecutive Successes in a Hoppe-Pólya Urn

Author:

Holst Lars

Abstract

In a sequence of independent Bernoulli trials the probability of success in the kth trial is p k = a / (a + b + k − 1). An explicit formula for the binomial moments of the number of two consecutive successes in the first n trials is obtained and some consequences of it are derived.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On Limited Length Binary Strings with an Application in Statistical Control;The Open Statistics & Probability Journal;2017-02-28

2. Counts of Bernoulli success strings in a multivariate framework;Statistics & Probability Letters;2016-12

3. On the number of runs for Bernoulli arrays;Journal of Applied Probability;2010-06

4. On Consecutive Records in Certain Bernoulli Sequences;Journal of Applied Probability;2009-12

5. A Note on Embedding Certain Bernoulli Sequences in Marked Poisson Processes;Journal of Applied Probability;2008-12

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