Parametric quantile regression models for fitting double bounded response with application to COVID-19 mortality rate data

TL;DR

This paper introduces two parametric quantile regression models using the power Johnson SB distribution to effectively model COVID-19 mortality rates within the unit interval, providing new tools for bounded response analysis.

Contribution

The paper develops and evaluates two fully parametric quantile regression models based on the power Johnson SB distribution for bounded responses, with application to COVID-19 mortality data.

Findings

Models accurately fit COVID-19 mortality rates across countries.

Simulation studies show reliable maximum likelihood estimators.

Diagnostic tools help assess model fit and influence.

Abstract

In this paper, we develop two fully parametric quantile regression models, based on power Johnson SB distribution Cancho et al. (2020), for modeling unit interval response at different quantiles. In particular, the conditional distribution is modelled by the power Johnson SB distribution. The maximum likelihood method is employed to estimate the model parameters. Simulation studies are conducted to evaluate the performance of the maximum likelihood estimators in finite samples. Furthermore, we discuss residuals and influence diagnostic tools. The effectiveness of our proposals is illustrated with two data set given by the mortality rate of COVID-19 in different countries.