Acta Scientiarum Naturalium Universitatis Pekinensis

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Some Results on a Counting Process Associated to Records

QI Yongcheng   

  1. Department of Probability & Statistics, Peking University,Beijing, 100871
  • Received:1996-04-12 Online:1997-05-20 Published:1997-05-20



  1. 北京大学概率统计系,北京,100871

Abstract: Let {In} be a sequence of the record indices, i.e, In, n≥1 are independent with P(In>=1)=1-P(In=0)=1/n for n≥1, and set u(n)nj=1Ij, n≥1. The probabilities P(|u(n)-logn|>εlogn) and P(u(n)=k) for some k's are inverstigated in the paper.

Key words: record index, Poisson approximation, convergence rate

摘要: 设{In}是一个记录指标序列, 即In, n≥1是独立随机变量, 满足P(In>=1)=1-P(In=0)=1/n, n≥1. 记u(n)nj=1Ij, 估计概率P(|u(n)-logn|>εlogn)和P(u(n)=k).

关键词: 记录指标, Poisson逼近, 收敛速度

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