Likelihood ratio test against simple stochastic ordering among several multinomial populations

摘要: Stochastic ordering between probability distributions has been widely studied in the past 50 years. Because it is often easy to make valuable judgments when such orderings exist, desirable recognize their existence and model distributional structures under them. Likelihood ratio test most commonly used method hypotheses involving stochastic orderings. Among various formally defined notions of ordering, least stringent simple ordering. In this paper, we consider testing hypothesis that all multinomial populations are identically distributed against alternative they We construct likelihood statistic for problem, provide limit form objective function corresponding show asymptotically as a mixture chi-squared distributions, i.e., chi-bar-squared distribution.