Solvency II will introduce economic risk-based solvency requirements for insurance companies across all European Member States for the first time. These new solvency requirements will be more risk-sensitive than in the past, thus enabling a better coverage of the real risks run by any particular insurer. Focusing only on technical risk, that has usually the greatest impact on the capital requirement for Non-Life insurers, particular attention need to be paid to estimate the distribution of aggregate claim amount. A collective risk model is usually chosen with a separate evaluation of frequency and severity distribution. At this regard many works show that standard parametric model does usually not provide an acceptable fit to both small and large claims of severity distribution. Focusing on a common case study (the Danish fire claims provided by McNeil), actuarial literature proposed several approaches based on the use of mixture and combined distributions calibrated with a Maximum Likelihood Approach. The target is to extend these results by exploring the performance of the Minimum Distance Approach (MD) to fit pure, mixtures and spliced distribution compared to Maximum Likelihood Approach. In particular we extend the classical MD approach by introducing alternative loss functions and weights on the empirical data. This topic is relevant in the actuarial literature in order to analyse the impact of a threshold to separate attritional and large claims in estimating the claim size distribution to be used for risk capital evaluation as requested in premium risk by Solvency II.