Related papers: The two parameters (k, r) in the generalized stati…
The reconstruction of the parameter of the model by the measurement of the random variable depending on this parameter is one of the main tasks of statistics. In the paper the notion of the statistically dual distributions is introduced.…
We show that the stochastic interpretation of Tsallis' thermostatistics given recently by Beck [Phys. Rev. Lett {\bf 87}, 180601 (2001)] leads naturally to a multi-parameter generalization. The resulting class of distributions is able to…
The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for…
In this paper, we investigate two-parameter entropies and obtain some conditions for their extensivity. By using a generalized $(k,r)-product$, correlations for subsystems are related to the joint probabilities, so that the entropy remains…
The properties of the nonextensive parameter q and the Tsallis distribution for self-gravitating systems are studied. A mathematical expression of q is deduced based on the generalized Boltzmann equation, the q-H theorem and the generalized…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…
We investigate a two-parameter entropy introduced by Schw\"{a}mmle and Tsallis and obtain its probability distribution in the canonical ensemble. The probability distribution is given in terms of the Lambert W-function which has been used…
The two parameter generalization of the complete elliptic integral of the second kind discussed recently by Barsan is expressed in terms of ordinary complete elliptic integrals.
Generalized superstatistics, i.e., a "statistics of superstatistics," is proposed. A generalized superstatistical system comprises a set of superstatistical subsystems and represents a generalized hyperensemble. There exists a random…
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)…
This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized…
A short review is given of how to apply the algebraic Heisenberg quantization scheme to a system of identical particles. For two particles in one dimension the approach leads to a generalization of the Bose and Fermi description which can…
The statistical parameters of five generalizations of the Lindley distribution, such as the average, variance and moments, are reviewed. A new double truncated Lindley distribution with three parameters is derived. The new distributions are…
We find the value of constants related to constraints in characterization of some known statistical distributions and then we proceed to use the idea behind maximum entropy principle to derive generalized version of this distributions using…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex…
We present a discussion of generalized statistics based on Renyi's, Fisher's and Tsallis's measures of information. The unifying conceptual framework which we employ here is provided by information theory. Important applications of…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…