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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)
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 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)
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)
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)
A problem in model selection, namely the identification of multiple change points for a piece-wise constant hazard rate, is discussed. A methodology using the Bayes' Information Criterion is developed in an overdispersed survival model (with corresponding quasi-likelihood function). The technique is used to identify changes in the historical frequency of(More)