New Quantile Regression Model for Unit Interval Regressands

This paper contributes significantly to regression analysis in that the authors have proposed a new and modern quantile regression (QR) model, which focuses exclusively on targeting regression analysis response variables that have a range on the unit interval (0, 1). The suggested model, which we call the Sine Unit Weibull (SUW) QR model, is constructed over a new trigonometric extension of the unit Weibull distribution—that is, one designed using the sin‐G family of distributions. The most important methodological contribution is the reparameterization of this new SUW distribution in terms of the distribution quantile function, which provides direct and flexible one‐to‐one correspondence with the explanatory variables and with the quantiles of the response variable through a logit link function. These are more robust for analyzing than the classic mean‐based regression, particularly where the data are asymmetrical or subject to outliers. The maximum likelihood technique is used to estimate the model parameters, and the estimators are shown to be consistent and accurate through a Monte Carlo simulation study, with the results indicating that bias and root mean square error are inversely proportional to sample size. The utility of the model utilizing three different real‐world datasets rigorously shows the practical usefulness and excellent performance of the SUW QR model. Checks of the fits of the randomized quantile residuals show an excellent fit, and tests with the information criteria confirm that the SUW QR model outperforms several well‐known competitive models of bounded data, including Kumaraswamy, unit‐Weibull, and Vasicek QR models, making it a strong new competitor in the bounded data modeling toolbelt.