Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis

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...

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Main Authors: Carlos A. dos Santos, Daniele C. T. Granzotto, Vera L. D. Tomazella, Francisco Louzada
Format: Article
Language:English
Published: MDPI AG 2018-03-01
Series:Journal of Risk and Financial Management
Subjects:
Online Access:http://www.mdpi.com/1911-8074/11/1/13
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spelling doaj-e068c1032f85476da66ab5b85320ab4e2020-11-24T22:40:13ZengMDPI AGJournal of Risk and Financial Management1911-80742018-03-011111310.3390/jrfm11010013jrfm11010013Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian AnalysisCarlos A. dos Santos0Daniele C. T. Granzotto1Vera L. D. Tomazella2Francisco Louzada3Department of Statistics, State University of Maringá, 87020-900 Maringá-PR, BrazilDepartment of Statistics, State University of Maringá, 87020-900 Maringá-PR, BrazilDepartment of Statistics, Federal University of São Carlos, 13565-905 São Carlos-SP, BrazilMath Science Institute and Computing, University of São Paulo, 13560-970 São Carlos-SP, BrazilIn 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.http://www.mdpi.com/1911-8074/11/1/13hierarchical Bayesian modelinfluential analysislog-logistic distributiontransmuted map
collection DOAJ
language English
format Article
sources DOAJ
author Carlos A. dos Santos
Daniele C. T. Granzotto
Vera L. D. Tomazella
Francisco Louzada
spellingShingle Carlos A. dos Santos
Daniele C. T. Granzotto
Vera L. D. Tomazella
Francisco Louzada
Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis
Journal of Risk and Financial Management
hierarchical Bayesian model
influential analysis
log-logistic distribution
transmuted map
author_facet Carlos A. dos Santos
Daniele C. T. Granzotto
Vera L. D. Tomazella
Francisco Louzada
author_sort Carlos A. dos Santos
title Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis
title_short Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis
title_full Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis
title_fullStr Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis
title_full_unstemmed Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis
title_sort hierarchical transmuted log-logistic model: a subjective bayesian analysis
publisher MDPI AG
series Journal of Risk and Financial Management
issn 1911-8074
publishDate 2018-03-01
description 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.
topic hierarchical Bayesian model
influential analysis
log-logistic distribution
transmuted map
url http://www.mdpi.com/1911-8074/11/1/13
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AT franciscolouzada hierarchicaltransmutedloglogisticmodelasubjectivebayesiananalysis
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