This note analyzes the distributional properties of Pareto Type III random variables. The orignal two parameters distribution proposed by Pareto is expanded in a three parameters version and both its density and characteristic function are derived. The analytic expression of the inverse...

This paper analyses the statistical distribution of war size. We find strong support for a Pareto-type distribution (power law) using data from different sources (COW and UCDP) and periods. A power law describesaccurately the size distribution of all wars, but also the distribution of the sample...

Using the Pareto distribution, this paper estimates the size distribution of metropolitan areas in India from 1981 through 2025. Empirical results offer evidence for dispersion of metropolitan population size, notwithstanding the growing concentration of urban population in metropolitan areas as...

This paper analyses the statistical distribution of war size. We find strong support for a Pareto-type distribution (power law) using data from different sources (COW and UCDP) and periods. A power law describesaccurately the size distribution of all wars, but also the distribution of the sample...

Basel II and Solvency 2 both use the Value-at Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log returns of financial assets. This is usually justified by the...

A simple model of the distribution of wealth is presented. In such a model the distribution of wealth follows a Pareto type II distribution whose parameters depend on the growth rates discussed in the book. Compared to previous studies of the asymptotic distribution of wealth in economies...

Basel II and Solvency 2 both use the Value-at Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log returns of financial assets. This is usually justified by the...

This short note analyzes the distributional properties of Pareto Type III random variables. We introduce a three parameters version of the orignal two parameters distribution proposed by Pareto and derive both the density and the characteristic function. The analytic expression of the inverse...

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the...

The city size distribution of many countries is remarkably well approximated by a Pareto distribution. We study what constraints this regularity imposes on standard urban models. We find that under general conditions urban models must have (i) a balanced growth path and (ii) a Pareto...