Burr type-XII as a superstatistical stationary distribution

Sánchez, Ewin

doi:10.1016/j.physa.2018.10.044

Cited by 8 publications

(3 citation statements)

References 12 publications

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“…Thereby, the overall probability defines the superstatistics of Gaussian statistics corresponding to different diffusivity packets. The above overall probability (Equation (4)) was analyzed in different scenarios in diffusion theory: (i) p(D) as a χ 2 gamma distribution in the context of random diffusivity, to compare with the diffusive diffusivity model [44], or to describe the movement of many individual small organisms that move with different diffusivities [54]; (ii) p(N) as a χ 2 -inverse gamma distribution that depends on particle size to investigate the aggregation and fragmentation process in the context of Laplace diffusion [50]; (iii) p(D) as a stretched exponential to construct a stretched Gaussian diffusion [17,55]; (iv) p(D) Lévy distribution to construct a Lévy process caused by large fluctuations in environment [52]; (v) p(β ∝ 1/T) as a Mittag-Leffler function to construct generalized Maxwell-Boltzmann distributions [56] and other generalized distributions [57,58], even as truncated-Mittag-Leffler function [59], which was applied in the analysis of the time series of oil price.…”

Section: From Log-normal Superstatistics To Brownian Yet Non-gaussianmentioning

confidence: 99%

Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

Santos

Menon

2020

Physics

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Superstatistical approaches have played a crucial role in the investigations of mixtures of Gaussian processes. Such approaches look to describe non-Gaussian diffusion emergence in single-particle tracking experiments realized in soft and biological matter. Currently, relevant progress in superstatistics of Gaussian diffusion processes has been investigated by applying χ2-gamma and χ2-gamma inverse superstatistics to systems of particles in a heterogeneous environment whose diffusivities are randomly distributed; such situations imply Brownian yet non-Gaussian diffusion. In this paper, we present how the log-normal superstatistics of diffusivities modify the density distribution function for two types of mixture of Brownian processes. Firstly, we investigate the time evolution of the ensemble of Brownian particles with random diffusivity through the analytical and simulated points of view. Furthermore, we analyzed approximations of the overall probability distribution for log-normal superstatistics of Brownian motion. Secondly, we propose two models for a mixture of scaled Brownian motion and to analyze the log-normal superstatistics associated with them, which admits an anomalous diffusion process. The results found in this work contribute to advances of non-Gaussian diffusion processes and superstatistical theory.

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Section: From Log-normal Superstatistics To Brownian Yet Non-gaussianmentioning

confidence: 99%

Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

Santos

Menon

2020

Physics

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“…Поиск распределений, заменяющих логнормальное распределение и объединяющих в себе свойства степенного и логнормального распределений, ведется на протяжении нескольких десятилетий (см., например, (Champernowne, 1956;Ghosh and Basu, 2019;Sánchez, 2019)). Аналитически простую двухпараметрическую модель PC, дающую широкий диапазон асимметрий, можно получить путем обобщения представленных в…”

Section: модель кривой паретоunclassified

Распределение Размеров Штатов, Округов И Городов США: Новая Информация О Форме Неравенства

Grachev¹

2020

Preprint

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В статье предлагается новый подход к исследованию закономерностей распределения размеров в системах расселения, основанный на анализе формы кривой Парето (PC). Для изучения формы PC использованы коэффициент Джини, асимметрии и, по аналогии с физикой фазовых переходов, показатель степени PC в окрестности нуля. Выполнен эмпирический анализ PC различных уровней агрегации системы расселения США. Форму распределения размеров штатов исследовали по десятилетиям с 1790 по 2010 год. Пространственный анализ формы PC округов и городов выполнен для 2010 года. Результаты проведенного эмпирического исследования показали, что PC штатов на протяжении 220 лет имела левостороннюю асимметрию. PC округов и городов имела как правостороннюю, так и левостороннюю асимметрию. Полученные результаты объясняют, в каких случаях распределение Парето, имеющее PC с правосторонней асимметрией, и логнормальное распределение с симметричной PC объективно могут не соответствовать реальным системам расселения. В качестве альтернативы степенному и логнормальному распределению рассмотрена аналитически простая двухпараметрическая модель с широким диапазоном асимметрии PC, объединяющая в себе свойства комбинации степенного и логнормального распределений. Верификация модели показала, что она адекватно описывает размеры поселений однородных систем расселения.

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“…The search for distributions that replace the lognormal distribution and combine the properties of the power-series distribution and lognormal distribution has been going on for several decades (for example, see (Champernowne, 1956;Ghosh and Basu, 2019;Sánchez, 2019)). An analytically simple two-parameter PC model that gives a wide range of asymmetries can be obtained by generalizing the single-parameter PCs presented in Table 1 (Antoniou et al, 2004):…”

Section: The Pareto Curve Modelmentioning

confidence: 99%

Size Distribution of States, Counties, and Cities in the USA: New Inequality Form Information

Grachev

2020

Preprint

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In this article, we propose a new approach for studying the patterns of size distribution in settlement systems, based on the analysis of the shape of the Pareto curve (PC). To study the shape of the PC, we used the Gini coefficient, the asymmetry coefficient, and, by analogy with the physics of phase transitions, critical exponent — the index of the PC degree in the neighborhood of zero. An empirical analysis of the PC of various levels of aggregation in the US settlement system has been performed. The form of size distribution of states was studied by decades from 1790 to 2010. The spatial analysis of the PC shape for counties and cities was performed for 2010. The results of an empirical study showed that the PC of the states had left-hand asymmetry over 220 years. The PC of districts and cities had both right-hand and left-hand asymmetries. The obtained results explain in which cases the Pareto distribution having a PC with right-hand asymmetry, and the lognormal distribution with a symmetric PC may not correspond objectively to real settlement systems. As an alternative to power-series distribution and lognormal distribution, we considered an analytically simple two-parameter model with a wide range of PC asymmetry that combines the properties of power-series distribution and lognormal distribution. Verification of the model showed that it adequately described the size of settlements in homogeneous settlement systems.

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Burr type-XII as a superstatistical stationary distribution

Cited by 8 publications

References 12 publications

Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

Распределение Размеров Штатов, Округов И Городов США: Новая Информация О Форме Неравенства

Size Distribution of States, Counties, and Cities in the USA: New Inequality Form Information

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