The Double Pareto-Lognormal Distribution—A New Parametric Model for Size Distributions

@article{Reed2001TheDP,
  title={The Double Pareto-Lognormal Distribution—A New Parametric Model for Size Distributions},
  author={William J. Reed and Murray Jorgensen},
  journal={Communications in Statistics - Theory and Methods},
  year={2001},
  volume={33},
  pages={1733 - 1753}
}
Abstract A family of probability densities, which has proved useful in modelling the size distributions of various phenomens, including incomes and earnings, human settlement sizes, oil-field volumes and particle sizes, is introduced. The distribution, named herein as the double Pareto-lognormal or dPlN distribution, arises as that of the state of a geometric Brownian motion (GBM), with lognormally distributed initial state, after an exponentially distributed length of time (or equivalently as… 
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References

SHOWING 1-10 OF 36 REFERENCES
A New Model Of Income Distribution: The Pareto-Lognormal Distribution
To describe the distributions of personal income, many models have been suggested as alternatives to the Pareto distribution. This paper is not intended to review the whole literature about such a…
Exponentially decreasing distributions for the logarithm of particle size
  • O. Barndorff-Nielsen
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1977
The family of continuous type distributions such that the logarithm of the probability (density) function is a hyperbola (or, in several dimensions, a hyperboloid) is introduced and investigated. It…
Asymmetric laplace laws and modeling financial data
On the Rank-Size Distribution for Human Settlements
An explanation for the rank-size distribution for human settlements based on simple stochastic models of settlement formation and growth is presented. Not only does the analysis of the model explain…
On the distribution of family names
Dynamic Models for File Sizes and Double Pareto Distributions
TLDR
The Recursive Forest File model, a new, dynamic generative user model that combines multiplicative models that generate lognormal distributions with recent work on random graph models for the web, explains the behavior of file size distributions, and may be useful for describing other power law phenomena in computer systems as well as other fields.
The Pareto law of incomes—an explanation and an extension
Lévy processes : theory and applications
Preface I. A tutorial on Levy processes Sato, K.: Basic results on Levy processes II. Distributional, pathwise and structural results Carmona, P. / Petit, F. / Yor, M.: Exponentials functionals of…
Application of Generalized Hyperbolic Lévy Motions to Finance
In standard mathematical finance, Brownian motion plays the dominating role as driving process for modelling price movements. In order to achieve a better fit to real-life data it is, however,…
A Model of Income Distribution
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and…
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