Heavy-tailed distributions for agent-based economic modelling

This chapter is devoted to the parametric statistical distributions of economic size phenomena of various types. Probability distributions of size variables are usually taken as the first quantitative characterization of complex systems, allowing one to detect the possible occurrence of regularities and to identify the underlying mechanisms at their origin - and thus at the origin of the behaviour of the complex system under study. A rapid survey covers the class of "heavy-tailed" distributions decreasing slower than exponentially at infinity. The fascination for "power laws" is then explained, starting from the statistical approaches for quantifying and testing a power-law distribution from your data, and ending with a (not exhaustive) list of mechanisms leading to power-law distributions. The description of distributions is ultimately enlarged by proposing the Laplace distribution, which has both tails - the upper and the lower - heavier than a standard Gaussian.