An Algorithm of a Longest of Runs Test for Very Long Sequences of Bernoulli Trials

by Alexander I. Kozynchenko .

Abstract: runs test is proposed for the case of equal probability Bernoulli trials processes. The algorithm is founded on the analysis of the event tree diagram, which has discovered the role of Fibonacci numbers of higher orders in counting the number of outcomes of interest in the sample space. Compared to the classical combinatorial formulas, the proposed algorithm provides the error-free exact probabilities and makes possible the processing of very long binomial data sets (up to 1000) on contemporary computers.

Key Words: Runs Tests, Longest Run, Bernoulli Trials, Fibonacci Numbers, Computing Algorithms

Author:
Alexander I. Kozynchenko, alexander_kozynchenko@yahoo.se

Editor: Wej-Min Huang, wh02@lehigh.edu

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