TY - JOUR

T1 - A new quantile regression for modeling bounded data under a unit birnbaum–saunders distribution with applications in medicine and politics

AU - Mazucheli, Josmar

AU - LEIVA SANCHEZ, VICTOR ELISEO

AU - Alves, Bruna

AU - Menezes, André F.B.

N1 - Funding Information:
Funding: Josmar Mazucheli gratefully acknowledges the partial financial support from Fundação Araucária (Grant 064/2019-UEM/Fundação Araucária), Brazil. The research of Víctor Leiva was partially supported by grant FONDECYT 1200525 from the National Agency for Research and Development (ANID) of the Chilean government under the Ministry of Science, Technology, Knowledge and Innovation.
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/4

Y1 - 2021/4

N2 - 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.

AB - 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.

KW - Birnbaum–Saunders distributions

KW - Data science

KW - Monte Carlo simulations

KW - R software

KW - Statistical modeling

UR - http://www.scopus.com/inward/record.url?scp=85104976585&partnerID=8YFLogxK

U2 - 10.3390/sym13040682

DO - 10.3390/sym13040682

M3 - Article

AN - SCOPUS:85104976585

VL - 13

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 4

M1 - 682

ER -