Testing homogeneity in a mixture of von Mises distributions with a structural parameter

The modified likelihood ratio test has been successfully applied for the homogeneity test in a variety of mixture models. In this paper, the authors propose the use of the modified likelihood ratio test and the iterative modified likelihood ratio test in general two-component von Mises mixture with a structural parameter. Two accuracy enhancing methods are developed. The limiting distributions of the resulting test statistics are derived. Simulations show that the test statistics have accurate type I errors and adequate power. A data set on orientations of turtles is analyzed, and the result suggests that there exist two subgroups of turtles that traveled in opposite directions. Title in French: we can supply this Résumé : Insérer votre résumé ici. The modified likelihood ratio test has been successfully applied for the homogeneity test in a variety of mixture models. In this paper, the authors propose the use of the modified likelihood ratio test and the iterative modified likelihood ratio test in general two-component von Mises mixture with a structural parameter. Two accuracy enhancing methods are developed. The limiting distributions of the resulting test statistics are derived. Simulations show that the test statistics have accurate type I errors and adequate power. A data set on orientations of turtles is analyzed, and the result suggests that there exist two subgroups of turtles that traveled in opposite directions.