Distribution of mann and whitney and allied statistics for two state Markov chain

Abstract

In this paper the distribution of transitions separated by 0,1,2,..r observations and also of T3,T4,and Tn for a Markov Chain having two states a and b has been discussed. The power of these statistics for comparing the randomness of a binomial sequence against a Markov chain alternative wherein the asymptotic probabilities of the two states are the same for the null hypothesis Ho(which is possible only when the alternative hypothesis is a Markov chain)has been considered. The relative efficiencies the various statistics show that the tests based on ab transitions separated by NKr observations(when K is fraction)will in general be better than Mann and Whitney statistics for testing two samples where the distributions are not known.