Polynomial power-Pareto quantile function models

In this paper we propose a polynomial power-Pareto quantile function model and a Bayesian method for parameters estimation. We also carried out simulation studies and applied our methodology to real data sets empirically. The results show that a quantile function approach to statistical modelling is very flexible due to the properties of quantile functions, and that the combination of a power and a Pareto distribution enables us to model both the main body and the tails of a distribution, even though the mathematical form of the distribution does not exist. Our research also suggests a new approach to studying extreme values based on a whole data set rather than group maximum/minimum or exceedances above/below a proper threshold value.