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Constraints for generalized mixtures of Weibull distributions with a common shape parameter

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  • Franco, Manuel
  • Vivo, Juana-María

Abstract

Weibull mixtures have been widely used in many applications, and they can be generalized by allowing negative mixing weights. In this note, we investigate constraints on the mixing weights and parameters of components under which the generalized mixture of Weibull distributions is a valid probability model, including the cases of exponential or Rayleigh components. In addition, characterizations are shown for generalized mixtures of three or fewer Weibull components. We use an example of a two-fold Weibull mixture model where negative weights are estimated, and the constraints are illustrated with a graphical example of three components.

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  • Franco, Manuel & Vivo, Juana-María, 2009. "Constraints for generalized mixtures of Weibull distributions with a common shape parameter," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1724-1730, August.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:15:p:1724-1730
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    1. Patra, Kaushik & Dey, Dipak K., 1999. "A multivariate mixture of Weibull distributions in reliability modeling," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 225-235, November.
    2. Carta, J.A. & Ramírez, P., 2007. "Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions," Renewable Energy, Elsevier, vol. 32(3), pages 518-531.
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