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Bayesian density estimation using skew student-t-normal mixtures

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  • Cabral, Celso Rômulo Barbosa
  • Bolfarine, Heleno
  • Pereira, José Raimundo Gomes

Abstract

We present a Bayesian approach for modeling heterogeneous data and estimate multimodal densities using mixtures of Skew Student-t-Normal distributions [Gómez, H.W., Venegas, O., Bolfarine, H., 2007. Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics 18, 395-407]. A stochastic representation that is useful for implementing a MCMC-type algorithm and results about existence of posterior moments are obtained. Marginal likelihood approximations are obtained, in order to compare mixture models with different number of component densities. Data sets concerning the Gross Domestic Product per capita (Human Development Report) and body mass index (National Health and Nutrition Examination Survey), previously studied in the related literature, are analyzed.

Suggested Citation

  • Cabral, Celso Rômulo Barbosa & Bolfarine, Heleno & Pereira, José Raimundo Gomes, 2008. "Bayesian density estimation using skew student-t-normal mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5075-5090, August.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5075-5090
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    References listed on IDEAS

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    Cited by:

    1. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
    2. Argiento, Raffaele & Guglielmi, Alessandra & Pievatolo, Antonio, 2010. "Bayesian density estimation and model selection using nonparametric hierarchical mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 816-832, April.
    3. Ahad Jamalizadeh & Tsung-I Lin, 2017. "A general class of scale-shape mixtures of skew-normal distributions: properties and estimation," Computational Statistics, Springer, vol. 32(2), pages 451-474, June.
    4. Fabrizio Ruggeri & Henrique Bolfarine & Jorge Luis Bazán & Reinaldo B. Arellano‐Valle & Victor Hugo Lachos Davila & Mário de Castro, 2021. "2021 International Statistical Institute Mahalanobis Award: A Tribute to Heleno Bolfarine," International Statistical Review, International Statistical Institute, vol. 89(3), pages 435-446, December.
    5. Fatma Zehra Doğru & Olcay Arslan, 2021. "Finite mixtures of skew Laplace normal distributions with random skewness," Computational Statistics, Springer, vol. 36(1), pages 423-447, March.

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