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Scale mixtures of normal distributions, i.e., mixtures of normal distributions on the variance parameters, have wide applications. The testing of homogeneity is one of the fundamental challenges in the application of scale mixtures of normal distributions. Recently, Chen and Li (Ann Stat 37:2523–2542, 2009) proposed a class of EM-tests for testing homogeneity in mixtures of normal distributions on...
In this paper, a new approach for testing fuzzy hypotheses based on likelihood ratio test statistic is presented. In this approach, we first formulate the hypotheses of interest by fuzzy sets, and then, a likelihood ratio statistic is defined based on the $$\delta $$ δ -cut of null fuzzy hypothesis. Also, in order to establish critical region, we give new definitions for the probabilities...
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