Unit Exponentiated Frechet Distribution: Actuarial Measures, Quantile Regression and Applications

In this study, a new distribution is developed for modelling responses on the unit interval. Several properties including moments, order statistics and stochastic ordering of the distribution are derived. Also, several actuarial measures, including risk measures and premium principles, are derived and Monte Carlo simulation studies performed on them. Different parameter estimation methods are used to estimate the parameters of the distribution. The performances of the estimators are assessed via Monte Carlo simulation studies. A quantile regression model is developed based on the distribution. Two different applications are carried out to assess the performance and usefulness of the distribution on both univariate data and data with covariates. The performance of both the distribution and its quantile regression model indicates that the new distribution can serve as an alternative to modelling actuarial data on unit interval.