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SQUARED COEFFICIENT OF VARIATION OF TAYLOR'S LAW FOR RANDOM ABSOLUTE DIFFERENCES

Published online by Cambridge University Press:  19 July 2017

Mark Brown  and
Joel E. Cohen
Mark Brown
Affiliation:
Department of Statistics, Columbia University, New York, NY 10027USA E-mail: [email protected]
Joel E. Cohen
Affiliation:
Laboratory of Populations, Rockefeller University, New York, NY 10065 USA; Earth Institute and Department of Statistics, Columbia University, New York, NY 10027 USA; Department of Statistics, University of Chicago, Chicago, IL 60637USA E-mail: [email protected]
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Abstract

In a family, parameterized by θ, of non-negative random variables with finite, positive second moment, Taylor's law (TL) asserts that the population variance is proportional to a power of the population mean as θ varies: σ2 (θ) = a[μ(θ)]b, a > 0. TL, sometimes called fluctuation scaling, holds widely in science, probability theory, and stochastic processes. Here we report diverse examples of TL with b = 2 (equivalent to a constant coefficient of variation) arising from a difference of random variables in normed vector spaces of dimension 1 and larger. In these examples, we compute a exactly using, in some cases, a simple, new technique. These examples may prove useful in future models that involve differences of random variables, including models of the spatial distribution and migration of human populations.

Keywords

coefficient of variationgeometric probabilitymigrationsignal-to-noise ratioTaylor's law
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 4 , October 2018 , pp. 483 - 494
Copyright
Copyright © Cambridge University Press 2017 

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