Numerical Procedures for Calculating the Probabilities of Recurrent Runs
Numerical Procedures for Calculating the Probabilities of Recurrent Runs作者机构：Department of Physics Trinity College Hartford USA
出 版 物：《Open Journal of Statistics》 (统计学期刊（英文）)
年 卷 期：2014年第4卷第2期
页 面：144-153页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Recurrent Events Theory of Runs Time Series Analysis Generating Functions Probability Distributions
摘 要：Run count statistics serve a central role in tests of non-randomness of stochastic processes of interest to a wide range of disciplines within the physical sciences, social sciences, business and finance, and other endeavors involving intrinsic uncertainty. To carry out such tests, it is often necessary to calculate two kinds of run count probabilities: 1) the probability that a certain number of trials results in a specified multiple occurrence of an event, or 2) the probability that a specified number of occurrences of an event take place within a fixed number of trials. The use of appropriate generating functions provides a systematic procedure for obtaining the distribution functions of these probabilities. This paper examines relationships among the generating functions applicable to recurrent runs and discusses methods, employing symbolic mathematical software, for implementing numerical extraction of probabilities. In addition, the asymptotic form of the cumulative distribution function is derived, which allows accurate runs statistics to be obtained for sequences of trials so large that computation times for extraction of this information from the generating functions could be impractically long.
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