On a new extreme value distribution: characterization, parametric quantile regression, and application to extreme air pollution events

Extreme-value distributions are important when modeling weather events, such as temperature and rainfall. These distributions are also important for modeling air pollution events. Particularly, the extreme-value Birnbaum-Saunders regression is a helpful tool in the modeling of extreme events. However, this model is implemented by adding covariates to the location parameter. Given the importance of quantile regression to estimate the effects of covariates along the wide spectrum of a response variable, we introduce a quantile extreme-value Birnbaum-Saunders distribution and its corresponding quantile regression model. We implement a likelihood-based approach for parameter estimation and consider two types of statistical residuals. A Monte Carlo simulation is performed to assess the behavior of the estimation method and the empirical distribution of the residuals. We illustrate the introduced methodology with unpublished real air pollution data.