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We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain…

Statistical Mechanics · Physics 2026-04-29 Lucas Squillante , Samuel M. Soares , Constantino Tsallis , Mariano de Souza

The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…

Statistical Mechanics · Physics 2025-03-10 Keisuke Okamura

The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' $q-$average of physical quantities, the sum $\sum…

Statistical Mechanics · Physics 2017-07-18 Ke-Ming Shen , Ben-Wei Zhang , En-Ke Wang

Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…

Statistical Mechanics · Physics 2009-11-13 Stefan Thurner , Rudolf Hanel

The XGamma distribution is a generated distribution from a mixture of Exponential and Gamma distributions. It is found that in many cases the XGamma has more flexibility than the Exponential distribution. In this paper we consider the sum…

Statistics Theory · Mathematics 2025-04-22 Therrar Kadri , Rahil Omairi , Khaled Smaili , Seifedine Kadry

Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…

Methodology · Statistics 2024-10-16 Sarah S. Ji , Benjamin B. Chu , Hua Zhou , Kenneth Lange

The factorization problem of $q$-exponential distribution within nonextensive statistical mechanics is discussed on the basis of Abe's general pseudoadditivity for equilibrium systems. it is argued that the factorization of compound…

Statistical Mechanics · Physics 2009-11-07 Qiuping A. Wang

Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…

Statistics Theory · Mathematics 2016-06-29 Gordon V. Chavez , Richard Kleeman

Exploring the analogy between quantum mechanics and statistical mechanics we formulate an integrated version of the Quantropy functional [1]. With this prescription we compute the propagator associated to Boltzmann-Gibbs statistics in the…

Statistical Mechanics · Physics 2019-07-09 Nana Cabo Bizet , César Damián Ascencio , Octavio Obregón , Roberto Santos-Silva

The sum of $N$ sufficiently strongly correlated random variables will not in general be Gaussian distributed in the limit N\to\infty. We revisit examples of sums x that have recently been put forward as instances of variables obeying a…

Statistical Mechanics · Physics 2009-11-13 H. J. Hilhorst , G. Schehr

Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular…

In this study it is shown that the Tsallis q-extended statistical theory was found efficient to describe faithfully the space plasmas statistics in every case, from the planetic magnetospheres, to solar corona and solar dynamics, as well as…

Chaotic Dynamics · Physics 2012-03-20 G. P. Pavlos

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they…

Statistical Mechanics · Physics 2009-11-07 Sumiyoshi Abe

This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al.…

Statistics Theory · Mathematics 2019-09-04 Mahendra Saha , Abhimanyu Singh Yadav , Arvind Pandey , Shivanshi Shukla , Sudhansu S Maiti

This paper establishes the optimal sub-Gaussian variance proxy for truncated Gaussian and truncated exponential random variables. The proofs rely on first characterizing the optimal variance proxy as the unique solution to a set of two…

Statistics Theory · Mathematics 2024-11-27 Mathias Barreto , Olivier Marchal , Julyan Arbel

The q-Gaussians are a class of stable distributions which are present in many scientific fields, and that behave as heavy tailed distributions for an especific range of q values. The identification of these values, which are used in the…

Data Analysis, Statistics and Probability · Physics 2015-06-11 E. L de Santa Helena , C. M. Nascimento , G. J. L. Gerhardt

In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parametrized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…

Statistical Mechanics · Physics 2007-05-23 John Evans , Fredrick Michael

The complex Gaussian distribution has been widely used as a fundamental spectral and noise model in signal processing and communication. However, its Gaussian structure often limits its ability to represent the diverse amplitude…

Machine Learning · Statistics 2026-03-30 Toru Nakashika

We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…

Astrophysics · Physics 2007-05-23 Luca Amendola

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