On Extensive Properties of Probability Distribution Functions in Non-Equilibrium States

On the Concavity of Multivariate Probability Distribution Functions on the Concavity of Multivariate Probability Distribution Functions

We prove that the multivariate standard normal probability distribution function is concave for large argument values. The method of proof allows for the derivation of similar statements for other types of multivariate probability distribution functions too. The result has important application, e.g., in probabilistic constrained stochastic programming problems.

Thermodynamic Properties of Non-Equilibrium States in Quantum Field Theory

Within the framework of relativistic quantum field theory, a novel method is established which allows to distinguish non-equilibrium states admitting locally a thermodynamic interpretation. The basic idea is to compare these states with global equilibrium states (KMS states) by means of local thermal observables. With the help of such observables, the states can be ordered into classes of incre...

On the Distribution of Natural Probability Functions

Evaluation of estimation methods for parameters of the probability functions in tree diameter distribution modeling

One of the most commonly used statistical models for characterizing the variations of tree diameter at breast height is Weibull distribution. The usual approach for estimating parameters of a statistical model is the maximum likelihood estimation (likelihood method). Usually, this works based on iterative algorithms such as Newton-Raphson. However, the efficiency of the likelihood method is not...

Lattice Boltzmann Method with regularized non-equilibrium distribution functions

The lattice Boltzmann (LB) model is a recent technique for the simulation and modeling of fluid flows [1– 5]. During the past fifteen years it has been successfully applied to many challenging problems in hydrodynamics as well as reaction-diffusion processes and wave propagation phenomena [6]. A particular shortcoming of this technique are numerical instabilities, that may develop at high Reyno...