Secant Unit Gompertz Quantile Regression for Modeling Bounded Endogenous Variables

Modeling data that falls within the [0,1] domain is a huge task in most scientific disciplines. This is because most classical distributions do not address the issues of complex data shapes as well as managing the dynamism of extreme quantiles. The study thus developed the secant-based extension of the unit Gompertz distribution; this distribution is a parametric and nonlinear quantile regression (QR) modeling strategy, which comes without the addition of parameters to the baseline distribution. The motivation behind this new approach lies in its use of trigonometric family of distributions, which enhances shape flexibility through the oscillating features that come with the use of trigonometric functions. This approach does not only simplify model construction, but helps to improve upon the data fitting capabilities of the new distribution. The proposed secant unit Gompertz (SUG) distribution's QR framework was attained through the method of reparameterization, where the probability density function (PDF) of the distribution was expressed in terms of its quantile function. The parameters of the distribution were derived using the maximum likelihood estimation procedure under a QR structure and the parameter estimators were shown to be consistent through Monte Carlo simulation analysis. A graphical examination of its PDF revealed that it presents attractive shapes such as skewed, J, reversed J and approximately symmetric, which clearly indicates that the new model can fit data exhibiting these traits. The model was applied to three real datasets to prove its practical usefulness to data from everyday life activities and the results revealed that the proposed SUG QR model consistently offered the best fit through information selection criteria and graphical diagnostics. The results also showed that the proposed model outperformed the unit Chen, unit Gompertz, the unit generalized half normal and the other four contending models in the area of heterogeneity across quantiles and shape flexibility. In conclusion, the study contributes significantly to the current state of knowledge as it has developed a trigonometric extension of the unit Gompertz distribution, broadening its versatility and parsimony in QR modeling involving diverse and intricate data structures.