The generalized lognormal distribution and the Stieltjes moment problem

This paper studies a Stieltjes-type moment problem defined by the generalized lognormal distribution, a heavy-tailed distribution with applications in economics, finance and related fields. It arises as the distribution of the exponential of a random variable following a generalized error distribution, and hence figures prominently in the EGARCH model of asset price volatility. Compared to the classical lognormal distribution it has an additional shape parameter. It emerges that moment (in)determinacy depends on the value of this parameter: for some values, the distribution does not have finite moments of all orders, hence the moment problem is not of interest in these cases. For other values, the distribution has moments of all orders, yet it is moment-indeterminate. Finally, a limiting case is supported on a bounded interval, and hence determined by its moments. For those generalized lognormal distributions that are moment-indeterminate Stieltjes classes of moment-equivalent distributions are presented.Comment: 12 pages, 1 figur

A Guide to the Dagum Distributions

In a series of papers in the 1970s, Camilo Dagum proposed several variants of a new model for the size distribution of personal income. This Chapter traces the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. It also provides interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution eld, including Lorenz curves and the Lorenz order and inequality measures. The Chapter ends with a survey of empirical applications of the Dagum distributions, many published in Romance language periodicals.

The Lorenz curve in economics and econometrics

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 ordering of multiparameter distributions in terms of their parameters, probability inequalities for distributions of quadratic forms, and Condorcet jury theorems.Lorenz curve, Lorenz order, majorization, income distribution, income inequality, statistical distributions, characterizations, Condorcet jury theorem.

Reproducible Econometric Simulations

Reproducibility of economic research has attracted considerable attention in recent years. So far, the discussion has focused on reproducibility of empirical analyses. This paper addresses a further aspect of reproducibility, the reproducibility of computational experiments. We examine the current situation in econometrics and derive a set of guidelines from our findings. To illustrate how computational experiments could be conducted and reported we present an example from time series econometrics that explores the finite-sample power of certain structural change tests.computational experiment, reproducibility, simulation, software.

Validating multiple structural change models : A case study

In a recent article, Bai and Perron (2003, Journal of Applied Econometrics) present a comprehensive discussion of computational aspects of multiple structural change models along with several empirical examples. Here, we report on the results of a replication study using the R statistical software package. We are able to verify most of their findings; however, some confidence intervals associated with breakpoints cannot be reproduced. These confidence intervals require computation of the quantiles of a nonstandard distribution, the distribution of the argmax functional of a certain stochastic process. Interestingly, the difficulties appear to be due to numerical problems in GAUSS, the software package used by Bai and Perron. --structural change,breakpoints,econometric software,numerical accuracy,reproducibility,R,GAUSS

Efficiency, Equity, and Generalized Lorenz Dominance

We decompose the generalized Lorenz order into a size and a distribution component. The former is represented by stochastic dominance, the latter by the standard Lorenz order. We show that it is always possible, given generalized Lorenz dominance between two distributions F and G, to find distributions H1 and H2 such that F stochastically dominates H1 and H1 Lorenz-dominates G, and such that F Lorenz-dominates H2 and H2 stochastically dominates G. We also show that generalized Lorenz dominance is characterized by this property and discuss the implications of these results for choice under risk.Income distribution, welfare dominance, Lorenz order, stochastic dominance, decisions under risk

Lorenz ordering of order statistics from log-logistic and related distributions

This paper obtains Lorenz ordering relationships among order statistics from log-logistic samples of possibly different sizes. Some results extend other families including the Lomax, Burr III and Burr XII distributions

The Lorenz curve in economics and econometrics

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 ordering of multiparameter distributions in terms of their parameters, probability inequalities for distributions of quadratic forms, and Condorcet jury theorems