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A family of probability densities, which has proved useful in modelling the size distributions of various phenomena, 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… (More)

- William Job 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 powerlaw behaviour, which is verified empirically for income and city-size data.

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)

- William Job Reed, Barry D. Hughes
- Journal of theoretical biology
- 2002

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)

- William Job Reed, Barry D. Hughes
- Physical review. E, Statistical, nonlinear, and…
- 2002

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)

- Albert B Phillimore, Chris D. Orme, +5 authors Ian P . F . Owens
- Evolution; international journal of organic…
- 2007

Theory predicts that biogeographic factors should play a central role in promoting population divergence and speciation. Previous empirical studies into biogeography and diversification have been relatively restricted in terms of the geographical area, phylogenetic scope, and the range of biogeographic factors considered. Here we present a global analysis… (More)

This paper examines the distribution of areas burned in forest fires. Empirical size distributions, derived from extensive fire records, for six regions in North America are presented. While they show some commonalities, it appears that a simple power-law distribution of sizes, as has been suggested by some authors, is too simple to describe the… (More)

- William Job 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)

- William Job Reed, Barry D. Hughes
- Mathematical biosciences
- 2004

This article deals with the theoretical size distribution of gene and protein families in complete genomes. A simple evolutionary model for the development of such families in which genes in a family are formed or selected against independently and at random, and in which new families are formed by the random splitting of existing families, is used to… (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)