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# Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis

1
Department of Statistics, State University of Maringá, 87020-900 Maringá-PR, Brazil
2
Department of Statistics, Federal University of São Carlos, 13565-905 São Carlos-SP, Brazil
3
Math Science Institute and Computing, University of São Paulo, 13560-970 São Carlos-SP, Brazil
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
J. Risk Financial Manag. 2018, 11(1), 13; https://doi.org/10.3390/jrfm11010013
Received: 30 December 2017 / Revised: 2 March 2018 / Accepted: 5 March 2018 / Published: 7 March 2018
(This article belongs to the Special Issue Extreme Values and Financial Risk)
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. View Full-Text
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MDPI and ACS Style

Dos Santos, C.A.; Granzotto, D.C.T.; Tomazella, V.L.D.; Louzada, F. Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis. J. Risk Financial Manag. 2018, 11, 13.

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