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Compounding or mixture distributions provide a rich class of models for applications ranging from models of heterogeneity, measurement error, distribution of stock returns and income to models of unemployment duration. Some very general mixtures will be considered which include many new mixture models and also provide a unified method of organizing and comparing previously considered model as well as a test of heterogeneity. These models are used to analyze CPS unemployment duration data. A heterogeneity interpretation of the mixture models explains the discrepancy between implications of search theory and patterns observed in aggregate unemployment data.