k -State Markov Chains

EXAMINATION of random sequences from Markov chains enables us to judge the relative efficiency of various methods which have been developed for testing different statistical hypotheses. A good deal of work, therefore, has been done recently by various authors 1–7 on the distribution of the number of transitions between adjoining observations of sequences from k -state Markov chains. The methods and results obtained in these investigations are rather unwieldy and cumbersome. The object of the present communication is to obtain the results for k -state chain from those of the two-state.