A non-uniform weighted two-components distribution is proposed in the present study for highly right skewed data modeling. We consider a G-GPD model that links a Gaussian distribution to a Generalized Pareto Distribution (GPD) at a junction point, with different weights for each component. It improves a G-GPD model with uniform weights that had been introduced in a preliminary study (see [1]). An iterative algorithm for parameters estimation is then provided, offering an accurate estimation of the Gaussian and GPD parameters, a judicious weighting of the model as well as a reliable position of the junction point, determined successfully in an unsupervised way. The performance of the iterative algorithm and the underlying new distribution, as compared with the existing G-GPD model, is studied on generated data and then on real extracellular neural recordings.