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Generalized mixtures of Weibull components

Author

Listed:
  • Manuel Franco
  • Narayanaswamy Balakrishnan
  • Debasis Kundu
  • Juana-María Vivo

Abstract

Weibull mixtures have been used extensively in reliability and survival analysis, and they have also been generalized by allowing negative mixing weights, which arise naturally under the formation of some structures of reliability systems. These models provide flexible distributions for modeling dependent lifetimes from heterogeneous populations. In this paper, we study conditions on the mixing weights and the parameters of the Weibull components under which the considered generalized mixture is a well-defined distribution. Specially, we characterize the generalized mixture of two Weibull components. In addition, some reliability properties are established for these generalized two-component Weibull mixture models. One real data set is also analyzed for illustrating the usefulness of the studied model. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Manuel Franco & Narayanaswamy Balakrishnan & Debasis Kundu & Juana-María Vivo, 2014. "Generalized mixtures of Weibull components," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 515-535, September.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:3:p:515-535
    DOI: 10.1007/s11749-014-0362-x
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    References listed on IDEAS

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    1. 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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    3. Karl Mosler & Christoph Scheicher, 2008. "Homogeneity testing in a Weibull mixture model," Statistical Papers, Springer, vol. 49(2), pages 315-332, April.
    4. 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.
    5. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    6. Farcomeni, Alessio & Nardi, Alessandra, 2010. "A two-component Weibull mixture to model early and late mortality in a Bayesian framework," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 416-428, February.
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    Cited by:

    1. Jorge Navarro, 2016. "Stochastic comparisons of generalized mixtures and coherent systems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 150-169, March.
    2. Nil Kamal Hazra & Maxim Finkelstein, 2018. "On stochastic comparisons of finite mixtures for some semiparametric families of distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 988-1006, December.
    3. F. G. Badía & Ji Hwan Cha, 2017. "On bending (down and up) property of reliability measures in mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 455-482, May.
    4. Serkan Eryilmaz, 2015. "Systems composed of two types of nonidentical and dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(5), pages 388-394, August.

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