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Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions

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  • Wan, Wai-Yin
  • Chan, Jennifer So-Kuen

Abstract

We propose a robust Poisson geometric process model with heavy-tailed distributions to cope with the problem of outliers as it may lead to an overestimation of mean and variance resulting in inaccurate interpretations of the situations. Two heavy-tailed distributions namely Student's t and exponential power distributions with different tailednesses and kurtoses are used and they are represented in scale mixture of normal and scale mixture of uniform respectively. The proposed model is capable of describing the trend and meanwhile the mixing parameters in the scale mixture representations can detect the outlying observations. Simulations and real data analysis are performed to investigate the properties of the models.

Suggested Citation

  • Wan, Wai-Yin & Chan, Jennifer So-Kuen, 2011. "Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 687-702, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:687-702
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    References listed on IDEAS

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    1. Jennifer Chan & Doris Leung, 2010. "Binary geometric process model for the modeling of longitudinal binary data with trend," Computational Statistics, Springer, vol. 25(3), pages 505-536, September.
    2. Lam Yeh & So Kuen Chan, 1998. "Statistical inference for geometric processes with lognormal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 27(1), pages 99-112, March.
    3. Choy, S.T. Boris & Chan, C.M., 2003. "Scale Mixtures Distributions in Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 93-104, May.
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    6. Chan, Jennifer S.K. & Boris Choy, S.T. & Makov, Udi E., 2008. "Robust Bayesian Analysis of Loss Reserves Data Using the Generalized-t Distribution," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 207-230, May.
    7. S. Choy & A. Smith, 1997. "Hierarchical models with scale mixtures of normal distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 205-221, June.
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    Cited by:

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    4. Chan, Jennifer So Kuen & Wan, Wai Yin, 2014. "Multivariate generalized Poisson geometric process model with scale mixtures of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 72-87.

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