Asymptotics for dependent Bernoulli random variables

Lan Wu, Yongcheng Qi and Jingping Yang

Statistics & Probability Letters, 2012, vol. 82, issue 3, 455-463

Abstract: This paper considers a sequence of Bernoulli random variables which are dependent in a way that the success probability of a trial conditional on the previous trials depends on the total number of successes achieved prior to the trial. The paper investigates almost sure behaviors for the sequence and proves the strong law of large numbers under weak conditions. For linear probability functions, the paper also obtains the strong law of large numbers, the central limit theorems and the law of the iterated logarithm, extending the results by James et al. (2008).

Keywords: Dependent Bernoulli random variables; Strong law of large numbers; Central limit theorem; Law of the iterated logarithm (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2011.12.002

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