Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble

G. Oshanin, Yu. Holovatch and G. Schehr

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 23, 4340-4346

Abstract: We study the distribution P(ω) of the random variable ω=x1/(x1+x2), where x1 and x2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution Ψ(x)∼ϕ(x)/x1+α, where α>0 is the Pareto index and ϕ(x) is the cut-off function. We consider two forms of ϕ(x): a bounded function ϕ(x)=1 for L≤x≤H, and zero otherwise, and a smooth exponential function ϕ(x)=exp(−L/x−x/H). In both cases Ψ(x) has moments of arbitrary order. We show that, for α>1, P(ω) always has a unimodal form and is peaked at ω=1/2, so that most probably x1≈x2. For 0<α<1 we observe a more complicated behavior which depends on the value of δ=L/H. In particular, for δ<δc–a certain threshold value–P(ω) has a three-modal (for a bounded ϕ(x)) and a bimodal M-shape (for an exponential ϕ(x)) form which signifies that in such ensembles the wealths x1 and x2 are disproportionately different.

Keywords: Pareto law; Paretian ensemble; Truncated wealth distribution; Fluctuations (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:23:p:4340-4346

DOI: 10.1016/j.physa.2011.06.067

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