用Stein-Chen方法给出了成功运行长度至少k的泊松近似的界

International Journal of Mathematical Analysis Pub Date : 1900-01-01 DOI:10.12988/IJMA.2019.81281

C. Sahatsathatsana

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引用次数: 0

摘要

得到了n (n≥1)次伯努利试验中k (k≥1)次成功的概率分布。注意到这个分布是k阶的二项分布，并说明了与之相关的几个未决问题。令Wn表示长度大于等于k的成功运行次数，并通过Stein-Chen耦合方法用泊松分布给出Wn的界。数学学科分类:60G07

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Bound on Poisson approximation on the length of success runs at least k by Stein-Chen method

The probability distribution of the number of success runs of the length k (k ≥ 1) in n (n ≥ 1) Bernoulli trials is obtained. It is noted that this distribution is a binomial distribution of the order k, and several open problems pertaining to it are stated. Let Wn denotes the number of success runs with the length k or more and we give bound for Wn by Poisson distribution via Stein-Chen coupling method. Mathematics Subject Classification: 60G07

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International Journal of Mathematical Analysis

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