Since the seminal work of Pareto, many empirical analyses suggested that the distribution of firms size is characterized by an asymptotic power like behavior. At the same time, recent investigations show that the distribution of annual growth rates of business firms displays a remarkable...

In this article we extend the agent-based model of firms’ formation and growth proposed in [4]. In [4] the firms‘ creation, expansion or contraction results from the interaction of heterogeneous utility maximizers. While the original model was able to replicate the power law distribution in...

Keynes (1911) derived general forms of probability density functions for which the “most probable value” is given by the arithmetic mean, the geometric mean, the harmonic mean, or the median. His approach was based on indirect (i.e., posterior) distributions and used a constant prior...

How do individuals shape societies? How do societies shape individuals? This paper develops a framework for studying the connections between micro and macro phenomena. The framework builds on two ingredients widely used in social science - population and variable. Starting with the simplest case...

We introduce a new 5-parameter family of distributions, the Asymmetric Exponential Power (AEP), able to cope with asymmetries and leptokurtosis and at the same time allowing for a continuous variation from non-normality to normality. We prove that the Maximum Likelihood (ML) estimates of the AEP...

Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a...

The objective of this paper is to extend the results on Pseudo Maximum Likelihood (PML) theory derived in Gourieroux, Monfort, and Trognon (GMT) (1984) to a situation where the first four conditional moments are specified. Such an extension is relevant in light of pervasive evidence that...

This paper contributes to characterizing the probability density of the price returns in some European day-ahead electricity markets (NordPool, APX, Powernext) by fitting some flexible and general families of distributions, such as the α-stable, Normal Inverse Gaussian (NIG), Exponential Power...

This paper surveys selected applications of the Lorenz curve and related stochastic orders in economics and econometrics, with a bias towards problems in statistical distribution theory. These include characterizations of income distributions in terms of families of inequality measures, Lorenz...

Power law behavior has been recognized to be a pervasive feature of many phenomena in natural and social sciences. While immense research efforts have been devoted to the analysis of behavioural mechanisms responsible for the ubiquity of power-law scaling, the strong theoretical foundation of...