A data driven runs test to identify first order positive Markovian dependence

作者：Corzo Jimmy A^*; Vergara Myrian E

来源：Hacettepe Journal of Mathematics and Statistics, 2016, 45(2): 521-540.

DOI：10.15672/HJMS.2015559562

• Markov-dependent Bernoulli trials
• Data driven runs test
• Runs distributions
• Hypothesis of randomness
• Power of a test

We propose a data driven test to identify first order positive Markovian dependence in a Bernoulli sequence, based on a combination of two runs tests: a well known runs test for the same purpose conditional on the numbers of ones in the sequence, and a modified runs test independent of the number of ones. We give analytic expressions for the exact distribution of the modified runs test statistic and for its power; also we built an algorithm to calculate it explicitly. To compare the power of the tests, we calculated these for some values of the proportion of ones and the success probability. We show that there are some intervals for the success probability in which the new runs test surpasses the power of the conditional test, and that the data driven test improves the power of the two runs tests, when they are considered separately.

• 出版日期2016-4