Statistics and Its Interface

Volume 13 (2020)

Number 1

Reference Bayesian analysis for the generalized lognormal distribution with application to survival data

Pages: 139 – 149

DOI: https://dx.doi.org/10.4310/SII.2020.v13.n1.a12

Authors

Vera L. D. Tomazella (Department of Statistics, Universidade Federal de São Carlos, São Paulo, Brazil)

Sandra R. de Jesus (Multidisciplinary Health Institute, Federal University of Bahia, Vitória da Conquista, Bahia, Brazil)

Francisco Louzada (Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, SP, Brazil)

Saralees Nadarajah (School of Mathematics, University of Manchester, United Kingdom)

Pedro L. Ramos (Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, SP, Brazil)

Abstract

This paper proposes a reference Bayesian approach for the estimation of the parameters of the generalized lognormal distribution in the presence of survival data. It is shown that the reference prior leads to a proper posterior distribution while the Jeffreys prior leads to an improper posterior. Simulation studies were performed to analyze the frequentist properties of credible intervals from the reference posterior distribution, considering complete and censored data. The proposed methodology is illustrated using two real datasets.

Keywords

Bayesian inference, generalized lognormal distribution, lognormal distribution, reference prior, Jeffreys prior, censored data

2010 Mathematics Subject Classification

Primary 62F15, 62N01. Secondary 62N05.

Received 20 September 2018

Published 7 November 2019