Statistical physics deals with systems composed of a large number of particles. The state of such systems is usually described by a distribution function, which allows us to determine the relevance of a certain configuration and to calculate macroscopic quantities, as the mean of physical observables. Gaussian distributions often occur whenever dealing with systems consisting of a large number of particles. These distributions well describe dynamics dominated by a large number of small random events, as for example the erratic motion of a small particle in water (Brownian motion). Not every system can however be described by Gaussian distributions, and there are situations in which the dynamics is dominated by rare and large fluctuations, in striking contrast with the Brownian motion corresponding to a Gaussian distribution. These large fluctuations result in long, power-law tail distributions, commonly termed Levy distributions. Associated to the long tail is the divergence of the first and/or second moment of these distibutions.