Brazilian Journal of Probability and Statistics

A new log-linear bimodal Birnbaum–Saunders regression model with application to survival data

Francisco Cribari-Neto and Rodney V. Fonseca

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Abstract

The log-linear Birnbaum–Saunders model has been widely used in empirical applications. We introduce an extension of this model based on a recently proposed version of the Birnbaum–Saunders distribution which is more flexible than the standard Birnbaum–Saunders law since its density may assume both unimodal and bimodal shapes. We show how to perform point estimation, interval estimation and hypothesis testing inferences on the parameters that index the regression model we propose. We also present a number of diagnostic tools, such as residual analysis, local influence, generalized leverage, generalized Cook’s distance and model misspecification tests. We investigate the usefulness of model selection criteria and the accuracy of prediction intervals for the proposed model. Results of Monte Carlo simulations are presented. Finally, we also present and discuss an empirical application.

Article information

Source
Braz. J. Probab. Stat., Volume 33, Number 2 (2019), 329-355.

Dates
Received: February 2017
Accepted: December 2017
First available in Project Euclid: 4 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1551690037

Digital Object Identifier
doi:10.1214/17-BJPS390

Keywords
Birnbaum–Saunders distribution diagnostic analysis model selection criteria prediction intervals misspecification test

Citation

Cribari-Neto, Francisco; Fonseca, Rodney V. A new log-linear bimodal Birnbaum–Saunders regression model with application to survival data. Braz. J. Probab. Stat. 33 (2019), no. 2, 329--355. doi:10.1214/17-BJPS390. https://projecteuclid.org/euclid.bjps/1551690037


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Supplemental materials

  • Supplement to “A new log-linear bimodal Birnbaum–Saunders regression model with application to survival data”. The supplementary material contains the following: an algorithm to compute confidence bands for the proposed residuals; an algorithm to compute prediction intervals; a Table with simulation results for the maximum likelihood estimators with bootstrap bias correction; and diagnostic plots of the empirical application.