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Homogeneity testing in a Weibull mixture model

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Abstract

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.

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Authors and Affiliations

  1. Seminar für Wirtschafts- und Sozialstatistik, Universität zu Köln, 50923, Köln, Germany

    Karl Mosler & Christoph Scheicher

Authors
  1. Karl Mosler
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  2. Christoph Scheicher
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Corresponding author

Correspondence to Karl Mosler.

Additional information

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.

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Mosler, K., Scheicher, C. Homogeneity testing in a Weibull mixture model. Statistical Papers 49, 315–332 (2008). https://doi.org/10.1007/s00362-006-0015-6

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  • DOI: https://doi.org/10.1007/s00362-006-0015-6

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