We aim at modelling fat-tailed densities whose distributions are unknown but are potentially asymmetric. In this context, the standard normality assumption is not appropriate.In order to make as few distributional assumptions as possible, we use a non-parametric algorithm to model the center of the distribution. Density modelling becomes more difficult as we move further in the tail of the distribution since very few observations fall in the upper tail area. Hence we decide to use the generalized Pareto distribution (GPD) to model the tails of the distribution. The GPD can approximate finite, exponential or subexponential tails. The estimation of the parameters of the GPD is based solely on the extreme observations. An observation is defined as being extreme if it is greater than a given threshold. The main difficulty with GPD modelling is to determine an appropriate threshold.