The authors show how the approach of Capéraà and Genest (Canad. J. Statist., 1990) can be used to order bivariate distributions with arbitrary marginals by their degree of dependence in the LTD (left-tail decreasing) or RTI (right-tail increasing) sense. Some properties of these new orderings are given, along with applications to Archimedean copulas, order statistics and compound random variables. RÉSUMÉ Les auteurs montrent comment l'approche de Capéraà et Genest (Revue canad. statist., 1990) peutêtre employée pour ordonner des lois bivariéesà marges quelconques selon leur force de dépendance au sens LTD (décroissance par ailes gauches) ou au sens RTI (croissance par ailes droites). Ils présentent quelques-unes des propriétés de ces ordres et en montrent l'intérêt pour l'étude des copules archimédiennes, des statistiques d'ordre et des sommes aléatoires.

We consider model-based clustering of data that lie on a unit sphere. Such data arise in the analysis of microarray experiments when the gene expressions are standardized so that they have mean 0 and variance 1 across the arrays. We propose to model the clusters on the sphere with inverse stereographic projections of multivariate normal distributions. The corresponding model-based clustering algorithm is described. This algorithm is applied first to simulated data sets to assess the performance of several criteria for determining the number of clusters and to compare its performance with existing methods and second to a real reference data set of standardized gene expression profiles.

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