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...

If business firms face a multiplicative growth process in which their growth rates are independent from their sizes, then these sizes cannot be distributed according to a stationary Pareto distribution. At the same time , the Laplace distribution of growth rates cannot be easily reconciled with...

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...

It is widely accepted that in liberalized electricity markets log-returns display fat-tailed densities. Besides qualitative assessments, so far precise characterizations of the shape of the distribution have been seldom provided. In this work, we characterize the conditional and unconditional...

If business firms face a multiplicative growth process in which their growth rates are independent from their sizes, then these sizes cannot be distributed according to a stationary Pareto distribution. At the same time , the Laplace distribution of growth rates cannot be easily reconciled with...

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...

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...

This paper performs an empirical analysis of the international cross sectional distribution of gross domestic product (GDP) growth rates and business cycles. We consider a balanced panel of 91 countries in the period 1960-2010 and two different measures of GDP fluctuations: the logarithmic...

Recent empirical analyses on different datasets have revealed a common exponential behaviour in the shape of the probability density of the corporate growth rates. We briefly review these analyses and present new evidence on this topic based on corporate data from Italian Manufacturing Industry....