Risk Indicators, Quantile Regression, and Applications of Exponentiated Tangent Burr XII Distribution

The continuous generation of data, which exhibit different characteristics, requires the creation of new distributions that best describe the traits of the data. The present study develops a new variant of the Burr XII distribution, referred to as the exponentiated tangent Burr XII distribution, specifically for the purposes of risk measurement. Plots of the density, hazard, and cumulative hazard rates show that the distribution supports various types of asymmetry and tail behavior, flexible hazard rates, including monotonic and nonmonotonic shapes. The moments and order statistics are derived and numerically estimated for the distribution. Risk indicators, including value-at-risk and tail value-at-risk, are also derived. These are numerically assessed via simulation studies. The results indicate that the distribution can be used to assess risk. The parameters of the distribution are estimated via maximum likelihood estimation method, and the properties of the estimators assessed via simulation studies. The results indicate that the estimators are consistent and asymptotically unbiased. A new quantile regression model is developed to inherit the features of the new distribution. The applications of the developed methodologies are demonstrated using insurance and tax revenue datasets. Risk indicators are estimated for the datasets. The developed methodologies outperformed Burr XII distribution and some of its extensions. The results indicate that the developed methodologies can be used for risk measurements.