Social scientists study two kinds of inequality: inequality between persons (as in income inequality) and inequality between subgroups (as in racial inequality). This paper analyzes the mathematical connections between the two kinds of inequality. The paper proceeds by exploring a set of...

This paper assesses the empirical validity of Zipf¿s Law for cities, using new data on 73countries and two estimation methods ¿ OLS and the Hill estimator. With either estimator,we reject Zipf¿s Law far more often than we would expect based on random chance; for 53out of 73 countries using OLS,...

We consider a compound-Poisson model with Pareto-type claims. In contrast to the classical case, where the claims are assumed to be iid., we assume that scaling and location parameters of the Pareto distribution follow a certain trend. We investigate the impact of this trend on parameter...

Operational losses are true dangers for banks since their maximal values to signal default are difficult to predict. This risky situation is unlike default risk whose maximum values are limited by the amount of credit granted. For example, our data from a very large US bank show that this bank...

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...

The Basel II accord encourages banks to develop their own advanced measurement approaches (AMA). However, the paucity of loss data implies that an individual bank cannot obtain a probability distribution with any reliability. We propose a model, targeting the regulator initially, by obtaining a...

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...