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A. M. Mood, F. A. Graybill and D. C. Boes, “Introduction to the Theory of Statistics,” 3rd Edition, McGraw-Hill, New York, 1974, pp. 540-541.

has been cited by the following article:

  • TITLE: Numerical Procedures for Calculating the Probabilities of Recurrent Runs

    AUTHORS: M. P. Silverman

    KEYWORDS: Recurrent Events; Theory of Runs; Time Series Analysis; Generating Functions; Probability Distributions

    JOURNAL NAME: Open Journal of Statistics, Vol.4 No.2, February 27, 2014

    ABSTRACT: 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.