On the fractal characterization of Paretian Poisson processes

Iddo I. Eliazar and Igor M. Sokolov

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 11, 3043-3053

Abstract: Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto’s law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of ‘fractal processes’ exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes–with respect to physical randomness-based measures of statistical heterogeneity–is characterized by exponential Poissonian intensities.

Keywords: Gini’s index; Pietra’s index; Evenness ratio; Min–max ratio; Moment ratio; Power-laws (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:11:p:3043-3053

DOI: 10.1016/j.physa.2012.01.030

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