Transport modelling of density profiles is usually described in terms of two coefficients in fusion plasmas: an effective Diffusivity (D) and an inward drift Delocity (V). Effective particle diffusivities are anomalous and it is usually accepted that anomalous transport is due to plasma turbulence. Evidence of inward drift velocities much larger than the value predicted by neoclassical theory has been recently reported. Peaked density profiles have been also reported in stellarator plasmas showing evidence of convective inward particle transport. Radially inward turbulent velocities have been observed in the plasma boundary region of fusion plasmas. From the theoretical point of view is has been argued that, in some cases, turbulence can give rise to a fully inward anomalous transport. Radially peaked profiles might be also explained on the basis of a description of turbulent transport in tokamaks by invariants. The importance of the statistical description of transport processes in fusion plasmas as an alternative approach to the traditional way to characterize transport based on the computation of effective transport coefficients (i.e. diffusion coefficients) and on average quantities (i.e., average correlation lengths) has been recently emphasized. Following this approach, we have investigated the Probability Density Function (PDF) of the effective radial velocity and radial scale of turbulent events as a strategy to identify the underlying physics of anomalous diffusivities and inward velocities in fusion plasmas.