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Related papers: Non-Gaussian distributions under scrutiny

200 papers

Non-Gaussian diffusion is commonly considered as a result of fluctuating diffusivity, which is correlated in time or in space or both. In this work, we investigate the non-Gaussian diffusion in static disordered media via a quenched trap…

Statistical Mechanics · Physics 2018-04-25 Liang Luo , Ming Yi

We show that whenever data are gathered using a device that performs a normalization-preprocessing, the ensuing normalized input, as recorded by the measurement device, will always be q-Gaussian distributed if the incoming data exhibit…

Statistical Mechanics · Physics 2007-08-23 C. Vignat , A. Plastino

The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…

Computation · Statistics 2023-05-19 Viktor Witkovský

The notion of generalised exponential family is considered in the restricted context of nonextensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown…

Statistical Mechanics · Physics 2009-11-13 Jan Naudts

Pearson's $\rho$ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a…

Statistics Theory · Mathematics 2018-09-28 Dag Tjøstheim , Håkon Otneim , Bård Støve

We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate…

Astrophysics · Physics 2009-12-30 Ruth Durrer , Roman Juszkiewicz , Martin Kunz , Jean-Philippe Uzan

The q-Gaussian is a probability distribution generalizing the Gaussian one. In spite of a q-normal distribution is popular, there is a problem when calculating an expectation value with a corresponding normalized distribution and not a…

Probability · Mathematics 2021-01-05 Nahla Ben Salah

A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian distribution of increments. Based on the…

Statistical Mechanics · Physics 2017-04-12 A. V. Chechkin , F. Seno , R. Metzler , I. M. Sokolov

Non-Gaussianity indicates complex dynamics related to extreme events or significant outliers. However, the correlation between non-Gaussianity and the dynamics of heterogeneous environments in anomalous diffusion remains uncertain. Inspired…

Soft Condensed Matter · Physics 2023-11-22 Haolan Xu , Xu Zheng , Xinghua Shi

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…

Statistics Theory · Mathematics 2022-08-04 Taras Bodnar , Dmitry Otryakhin , Erik Thorsen

Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon's entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made…

Statistical Mechanics · Physics 2007-05-23 Jan Naudts

The q-Gaussian function emerges naturally in various applications of statistical mechanics of non-ergodic and complex systems. In particular it was shown that in the theory of binary processes with correlations, the q-Gaussian can appear as…

Mathematical Physics · Physics 2013-01-17 Angel Akio Tateishi , Rudolf Hanel , Stefan Thurner

The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that…

Probability · Mathematics 2015-05-14 Marjorie G. Hahn , Xinxin Jiang , Sabir Umarov

We advance scale-invariance arguments for systems that are governed (or approximated) by a $q-$Gaussian distribution, i.e., a power law distribution with exponent $Q=1/(1-q); q \in \mathbb{R}$. The ensuing line of reasoning is then compared…

Statistical Mechanics · Physics 2009-11-11 C. Vignat , A. Plastino

Due to gravitational instability, an initially Gaussian density field develops non-Gaussian features as the Universe evolves. The most prominent non-Gaussian features are massive haloes, visible as clusters of galaxies. The distortion of…

Astrophysics · Physics 2015-06-24 Guido Kruse , Peter Schneider

The emergence of non-gaussian distributions for macroscopic quantities in nonequilibrium steady states is discussed with emphasis on the effective criticality and on the ensuing universality of distribution functions. The following problems…

Statistical Mechanics · Physics 2009-11-10 Zoltan Racz

Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…

General Relativity and Quantum Cosmology · Physics 2021-01-20 Eileen Giesel , Robert Reischke , Björn Malte Schäfer , Dominic Chia

By a non-Gaussian integral we mean integral of the product of an arbitrary function and exponent of a polynomial. We develop a theory of such integrals, which generalizes and simplifies the theory of general hypergeometric functions in the…

General Mathematics · Mathematics 2020-10-20 Alexander Roi Stoyanovsky

We formulate the statistics of peaks of non-Gaussian random fields and implement it to study the sphericity of peaks. For non-Gaussianity of the local type, we present a general formalism valid regardless of how large the deviation from…

Cosmology and Nongalactic Astrophysics · Physics 2025-09-03 Cristiano Germani , Mohammad Ali Gorji , Michiru Uwabo-Niibo , Masahide Yamaguchi

Robert Cousins has posted a comment on my manuscript on ``Confidence intervals for the Poisson distribution''. His key point is that one should not include in the likelihood non-physical parameter values, even for frequency statistics. This…

Data Analysis, Statistics and Probability · Physics 2025-11-04 Frank C. Porter