On the fractal characterization of Paretian Poisson processes

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...

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Veröffentlicht in:Physica A 2012-06, Vol.391 (11), p.3043-3053
Hauptverfasser: Eliazar, Iddo I., Sokolov, Igor M.
Format: Artikel
Sprache:eng
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Zusammenfassung: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. ► The statistical heterogeneity of Poissonian populations is studied. ► Statistical heterogeneity is measured via an array of socioeconomic evenness gauges. ► Paretian Poisson processes emerge as ‘fractal’ with respect to the measurements.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2012.01.030