Homogeneity testing in a Weibull mixture model

The mixed Weibull distribution provides a flexible model to analyze random durations in a possibly heterogeneous population. To test for homogeneity against unobserved heterogeneity in a Weibull mixture model, a dispersion score test and a goodness-of-fit test are investigated. The empirical power of these tests is assessed and compared on a broad range of alternatives. It comes out that the dispersion score test, as it is based on a Weibull-to-exponential transformation, often breaks down. A simple new procedure is introduced for Weibull mixtures in scale, which combines the dispersion score test and the goodness-of-fit test. The new test is compared with several known procedures and shown to have a good overall power. To detect mixtures in shape and scale, a goodness-of-fit test is recommended. This research has been partially sponsored by a grant of the Deutsche Forschungsgemeinschaft. We thank Lars Haferkamp for computational assistance and Wilfried Seidel and a referee for their remarks on alternative test procedures.