A new quantile regression for modeling bounded data under a unit birnbaum–saunders distribution with applications in medicine and politics

Josmar Mazucheli, VICTOR ELISEO LEIVA SANCHEZ, Bruna Alves, André F.B. Menezes

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Quantile regression provides a framework for modeling the relationship between a response variable and covariates using the quantile function. This work proposes a regression model for continuous variables bounded to the unit interval based on the unit Birnbaum–Saunders distribution as an alternative to the existing quantile regression models. By parameterizing the unit Birnbaum–Saunders distribution in terms of its quantile function allows us to model the effect of covariates across the entire response distribution, rather than only at the mean. Our proposal, especially useful for modeling quantiles using covariates, in general outperforms the other competing models available in the literature. These findings are supported by Monte Carlo simulations and applications using two real data sets. An R package, including parameter estimation, model checking as well as density, cumulative distribution, quantile and random number generating functions of the unit Birnbaum–Saunders distribution was developed and can be readily used to assess the suitability of our proposal.

Original languageEnglish
Article number682
JournalSymmetry
Volume13
Issue number4
DOIs
StatePublished - Apr 2021
Externally publishedYes

Keywords

  • Birnbaum–Saunders distributions
  • Data science
  • Monte Carlo simulations
  • R software
  • Statistical modeling

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