A New Quantile Regression for Modeling Bounded Data under a Unit Birnbaum–Saunders Distribution with Applications in Medicine and Politics

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.

The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model

“…[25] introduced the Kumaraswamy quantile regression model for the dependent variables on the (0, 1) interval. The presented idea in the study of [25] has been applied to different probability distributions by [9,11,12,14,[26][27][28][29].…”

“…Similarly, [8] used X = T/(T + 1) transformation on the improved second-degree Lindley (ISDL) distribution and resulting distribution was called as unit-ISDL distribution. These approaches have been used many authors such as [9][10][11][12][13][14][15][16][17][18][19] and so on.…”

A Note on the Birnbaum–Saunders Conditionals Model

“…The BS distribution, which is asymmetric, was initially introduced as a suitable model for lifetimes in fatigue settings (see Leiva [1] and Balakrishnan and Kundu [2]). Other recent extensions of the BS model are delivered in the works of Reyes et al [3], Martínez-Flórez et al [4], Gómez-Déniz and Gómez [5] and Mazucheli et al [6], among others. However, it has also been shown to function as a suitable model for other non-negative variables.…”

A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

“…In this case, the relation between the response and covariates utilizing the mean is not suitable since it is strongly affected by asymmetry and atypical observations. Another limitation of the usual regression approach is when we are interested in studying other parameters in addition to the mean; see [1,2].…”

“…Goodness-of-fit techniques for a determined model permit us to evaluate the adequacy of the model to the data; see [18]. The pseudo-R 2 proposed by [19]-from now denoted as R 2 M -and randomized quantile (RQ) and generalized Cox-Snell (GCS) residuals are helpful tools for evaluating goodness of fit; see [20,21]. Local influence assesses the effect of small perturbations in the data and/or model assumptions on parameter estimates; see [22].…”