The exponentially truncated q-distribution: A generalized distribution for real complex systems

TL;DR

This paper introduces a new generalized distribution, the exponentially truncated q-distribution, which has finite variance and effectively models power law behaviors in various real complex systems, overcoming limitations of traditional distributions.

Contribution

The paper proposes a novel generalized distribution that accounts for finite variance in power law systems, extending non-extensive thermodynamics to practical applications.

Findings

Good fit for financial, geophysical, and social data

Accurately models entire probability density functions

Shows universal size limiting behavior in complex systems

Abstract

To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus can not be used as a standard distribution. Normally professionals in the area use normal distribution with variable parameters or some other approximate distribution like Gumbel, Wakeby, or Pareto, which has limited validity. Tsallis presented a microscopic theory of power law in the framework of non-extensive thermodynamics considering long-range interactions or long memory. In the present work, we consider softing of long-range interactions or memory and presented a generalized distribution which have finite variance and can be used as a standard distribution for all real complex systems with power law behaviour. We applied this distribution for a financial system, rain precipitation and some geophysical and social systems. We found a good agreement for entire range in all cases for the probability density function (pdf) as well as the accumulated probability. This distribution shows universal nature of the size limiting in real systems.