Latin America was one of the hotspots of COVID-19 during the pandemic. Therefore, understanding the COVID-19 mortality rate in Latin America is crucial, as it can help identify at-risk populations and evaluate the quality of healthcare. In an effort to find a more flexible and suitable model, this work formulates a new quantile regression model based on the unit ratio-Weibull (URW) distribution, aiming to identify the factors that explain the COVID-19 mortality rate in Latin America. We define a systematic structure for the two parameters of the distribution: one represents a quantile of the distribution, while the other is a shape parameter. Additionally, some mathematical properties of the new regression model are presented. Point and interval estimates of maximum likelihood in finite samples are evaluated through Monte Carlo simulations. Diagnostic analysis and model selection are also discussed. Finally, an empirical application is presented to understand and quantify the effects of economic, social, demographic, public health, and climatic variables on the COVID-19 mortality rate quantiles in Latin America. The utility of the proposed model is illustrated by comparing it with other widely explored quantile models in the literature, such as Kumaraswamy and unit Weibull regressions.

The present work proposes a new class of model for random variables with support in the positive real line, this model explains the conditional quantile and is an alternative for modeling data that indicate asymmetric behavior and heavy tails. We present a new autoregressive moving average model based on the $\tau$–th quantile of the Burr XII distribution (BXII-ARMA) since the quantile is less sensitive than the average of heterogeneous populations and also suitable in the presence of outliers. This model makes it possible to model any quantile by a dynamic structure containing autoregressive terms and moving averages, time-varying regressors, unknown parameters, and a link function. The conditional maximum likelihood method is considered to estimate the parameters and build the confidence intervals of the BXII-ARMA model. In addition, the model is adjusted to real data related to the financial market and compared with other competing models.