On the Asymptotic Distribution of the "PSI-Squared" Goodness of Fit Criteria for Markov Chains and Markov Sequences

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. 1. Introduction and summary. The use of a statistic of the algebraic form of Pearson's chi-squared as a measure of goodness of fit for frequencies from a fully specified mth order stationary Markov chain was first discussed and con-trasted with the appropriate likelihood ratio criterion by Bartlett [2]. Since the distribution of the former statistic is not that of a tabular x2-variate, it and allied statistics, are sometimes described as "psi-squared" statistics. Patankar [141 derived the approximate asymptotic distribution (as the total number of