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- William J. Reed
- 2001

Many empirical size distributions in economics and elsewhere exhibit power-law behaviour in the upper tail. This article contains a simple explanation for this. It also predicts lower-tail power-law behaviour, which is verified empirically for income and city-size data. Many empirical distributions encountered in economics and other realms of inquiry… (More)

whose support and hospitality are gratefully acknowledeged. Abstract A family of probability densities, which has proved useful in modelling the size distributions of various phenomena, including incomes and earnings, human settlement sizes, oilfield volumes and particle sizes, is introduced. The distribution, named herein as the double Pareto-lognormal or… (More)

This paper considers the consequences of an avoidable risk of irreversible environmental catastrophe for society's optimal long-run consumption/pollution tradeoffs. The risk is assumed to be a nondecreasing function of pollution concentration which evolves as a dynamic environmental renewal process. The main objective of the paper is to derive qualitative… (More)

This article deals with the theoretical size (number of species) distribution of live genera, arising from a simple model of macroevolution in which speciations and extinctions are assumed to occur independently and at random, and in which new genera are formed by the random splitting of existing genera. Mathematically, the distribution is that of the state… (More)

We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law… (More)

- William J. Reed
- 2004

The normal-Laplace (NL) distribution results from convolving independent normally distributed and Laplace distributed components. It is the distribution of the stopped state of a Brownian motion with normally distributed starting value if the stopping hazard rate is constant. Properties of the NL distribution discussed in the article include its shape and… (More)

We present a model for the distribution of family names that explains the power-law decay of the probability distribution for the number of people with a given family name. The model includes a description of the process of generation or importation of new names, and a description of the growth of the number of individuals with a name, and corresponds for a… (More)

We discuss a class of models for the evolution of networks in which new nodes are recruited into the network at random times, and links between existing nodes that are not yet directly connected may also form at random times. The class contains both models that produce "small-world" networks and less tightly linked models. We produce both trees, appropriate… (More)

A possible explanation for the frequent occurrence of power-law distributions in biology and elsewhere comes from an analysis of the interplay between random time evolution and random observation or killing time. If the system population or its topological parameters grow exponentially with time, and observations on the system correspond to stopping the… (More)