Exact and approximate runs distributions
Exact and approximate runs distributions
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精确和近似运行分布
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
Michelle C. Gornowicz
中科院分区：
文献类型：
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作者：
A. Godbole;Michelle C. Gornowicz
让R = RN表示n bernoulll（p）试验序列的总数（和无条件）的成功或失败的数量，其中p在整个过程中都是已知的。带有参数p和q的负二项式随机变量（= 1 -p）。 ½）。由于限制支持集是一组奇数整数，因此在最后一个结果中找到了总变化误差界（o（p）的总变化。
Let R = Rn denote the total (and unconditional) number of runs of successes or failures in a sequence of n Bernoulll (p) trials, where p is assumed to be known throughout. The exact distribution of R is related to a convolution of two negative binomial random variables with parameters p and q (=1-p). Using the representation of R as the sum of 1 - dependent indicators, a Berry - Esseen theorem is derived; the obtained rate of sup norm convergence is O(n-½). This yields an unconditional version of the classical result of Wald and Wolfowitz (1940). The Stein - Chen method for m - dependent random variables is used, together with a suitable coupling, to prove a Poisson limit theorem for R. but with the limiting support set being the set of odd integers, Total variation error bounds (of order O(p) are found for the last result. Applications are indicated.