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Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis

Author

Listed:
  • Carlos A. Dos Santos

    (Department of Statistics, State University of Maringá, 87020-900 Maringá-PR, Brazil
    These authors contributed equally to this work.)

  • Daniele C. T. Granzotto

    (Department of Statistics, State University of Maringá, 87020-900 Maringá-PR, Brazil
    These authors contributed equally to this work.)

  • Vera L. D. Tomazella

    (Department of Statistics, Federal University of São Carlos, 13565-905 São Carlos-SP, Brazil
    These authors contributed equally to this work.)

  • Francisco Louzada

    (Math Science Institute and Computing, University of São Paulo, 13560-970 São Carlos-SP, Brazil
    These authors contributed equally to this work.)

Abstract

In this study, we propose to apply the transmuted log-logistic (TLL) model which is a generalization of log-logistic model, in a Bayesian context. The log-logistic model has been used it is simple and has a unimodal hazard rate, important characteristic in survival analysis. Also, the TLL model was formulated by using the quadratic transmutation map, that is a simple way of derivating new distributions, and it adds a new parameter λ , which one introduces a skewness in the new distribution and preserves the moments of the baseline model. The Bayesian model was formulated by using the half-Cauchy prior which is an alternative prior to a inverse Gamma distribution. In order to fit the model, a real data set, which consist of the time up to first calving of polled Tabapua race, was used. Finally, after the model was fitted, an influential analysis was made and excluding only 0.1 % of observations (influential points), the reestimated model can fit the data better.

Suggested Citation

  • Carlos A. Dos Santos & Daniele C. T. Granzotto & Vera L. D. Tomazella & Francisco Louzada, 2018. "Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis," JRFM, MDPI, vol. 11(1), pages 1-12, March.
    • Handle: RePEc:gam:jjrfmx:v:11:y:2018:i:1:p:13-:d:135071
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    References listed on IDEAS

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    1. Juliana Fachini & Edwin Ortega & Francisco Louzada-Neto, 2008. "Influence diagnostics for polyhazard models in the presence of covariates," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(4), pages 413-433, October.
    2. Sik-Yum Lee, 2006. "Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 541-564, September.
    3. Lee, Sik-Yum & Lu, Bin & Song, Xin-Yuan, 2006. "Assessing local influence for nonlinear structural equation models with ignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1356-1377, March.
    4. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
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    Cited by:

    1. Stephen Chan & Saralees Nadarajah, 2020. "Extreme Values and Financial Risk," JRFM, MDPI, vol. 13(2), pages 1-3, February.

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