Success run statistics defined on an urn model
Success run statistics defined on an urn model
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在 urn 模型上定义的成功运行统计数据
DOI：
10.1239/aap/1198177236
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发表时间：
2007
影响因子：
1.2
通讯作者：
Z. Psillakis
中科院分区：
文献类型：
--
作者：
F. S. Makri;Andreas N. Philippou;Z. Psillakis
考虑表示长度完全等于且至少等于固定长度的成功运行的数目以及长度大于或等于特定长度的成功运行的长度之和的统计。它们定义在线性和循环有序的二元序列上，根据Pólya-Eggenberger骨灰盒模型得出。与线性序列中的长度和统计量相关的等待时间也被检验。通过一个简单的统一组合方法，得到了以二项式系数表示的精确的边缘分布函数和联合概率分布函数。平均值也是以闭合形式导出的。在给定序列成功次数的情况下，给出了条件分布的计算易于处理的公式，这些公式在随机性的非参数检验中很有用。利用所研究的统计量的特定概率，推导出某些连续系统的最长成功运行长度和可靠性的分布。文中给出了数值算例，以说明理论结果。
Statistics denoting the numbers of success runs of length exactly equal and at least equal to a fixed length, as well as the sum of the lengths of success runs of length greater than or equal to a specific length, are considered. They are defined on both linearly and circularly ordered binary sequences, derived according to the Pólya-Eggenberger urn model. A waiting time associated with the sum of lengths statistic in linear sequences is also examined. Exact marginal and joint probability distribution functions are obtained in terms of binomial coefficients by a simple unified combinatorial approach. Mean values are also derived in closed form. Computationally tractable formulae for conditional distributions, given the number of successes in the sequence, useful in nonparametric tests of randomness, are provided. The distribution of the length of the longest success run and the reliability of certain consecutive systems are deduced using specific probabilities of the studied statistics. Numerical examples are given to illustrate the theoretical results.