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We present the data on wealth and income distributions in the United Kingdom, as well as on the income distributions in the individual states of the USA. In all of these data, we find that the great majority of population is described by an…
It is shown that power law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium which are expected to occur in collisionless plasmas containing fully developed quasi-stationary turbulence.…
In this paper we introduce a new method to add a parameter to a family of distributions. The additional parameter is completely studied and a full description of its behaviour in the distribution is given. We obtain several mathematical…
The total number of fatalities of an epidemic outbreak is a dramatic but extremely informative quantity. Knowledge of the statistics of this quantity allows the calculation of the mean total number of fatalities conditioned to the fact that…
Systems described by equations involving both multiplicative and additive noise are common in nature. Examples include convection of a passive scalar field, polymersin turbulent flow, and noise in dye lasers. In this paper the one component…
In this paper we present various new inequalities for tail proabilities for distributions that are elements of the most improtant exponential families. These families include the Poisson distributions, the Gamma distributions, the binomial…
The notion of entropy penetrates much of science. A key feature of the all-important notion of Boltzmann-Gibbs-Shannon entropy is its extensivity (additivity over independent subsystems). However, there is a need for other quantities. In…
We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…
For a plasma with fixed total energy, number of particles, and momentum, the distribution function that maximizes entropy is a Boltzmann distribution. If, in addition, the rearrangement of charge is constrained, as happens on ion-ion…
We study a modified version of a model previously proposed by Jackson and Wolinsky to account for communicating information and allocating goods in socioeconomic networks. In the model, the utility function of each node is given by a…
A new three-parameter cumulative distribution function defined on $(\alpha,\infty)$, for some $\alpha\geq0$, with asymmetric probability density function and showing exponential decays at its both tails, is introduced. The new distribution…
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…
The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this letter, we…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
A class of conserved models of wealth distributions are studied where wealth (or money) is assumed to be exchanged between a pair of agents in a population like the elastically colliding molecules of a gas exchanging energy. All sorts of…
We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…
Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution,…
Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered as an important property of these systems. In general, power law exists in the central part of the distribution. It has…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution…