期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2019
卷号：83
期号：1
页码：143-154
DOI：10.1007/s13171-019-00176-1
出版社：Indian Statistical Institute
摘要：In this paper, we prove the asymptotic normality of the conditional distribution of the number of runs given the number of successes for a sequence of independent Bernoulli random variables. In our proof, the Frobenius-Harper technique is used to represent the number of runs as the sum of independent and not necessarily identically distributed Bernoulli random variables. Then, an asymptotic conditional test for independence is provided. Our simulation results exhibit that the test based on conditional distribution performs better that one based on unconditional distribution, over the entire range of success probability and first order correlation. In addition, the UMVUEs of the factorial moments and the probabilities of the number of runs are presented in this paper.
关键词：Binary data;Factorial moment;Frobenius-Harper technique;Number of runs;Probability distribution;Test of independence
