Related papers: Loading loss-cone distributions in particle simula…
Numerical procedures for generating non-Maxwellian velocity distributions in particle simulations are presented. First, Monte Carlo methods for an $(r,q)$ distribution that generalizes flattop and kappa distributions are discussed. Then,…
We demonstrate that a nonthermal distribution of particles described by a kappa distribution can be accurately approximated by a weighted sum of Maxwell-Boltzmann distributions. We apply this method to modeling collision processes in…
Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte-Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed.…
A simple numerical method for loading of a relativistic Maxwellian-type distribution is proposed based on inverse transform sampling. The relativistic Maxwellian energy distribution is introduced as an alternative to the Maxwell-J\"{u}ttner…
A procedure for generating random variates from a relativistic Maxwellian distribution with arbitrary temperature and drift velocity is presented. The algorithm is based on the rejection method and can be used to initialize particle…
Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation…
A random number generator for the Kappa velocity distribution in particle simulations is proposed. Approximating the cumulative distribution function with the q-exponential function, an inverse transform procedure is constructed. The…
The histogram estimator of a discrete probability mass function often exhibits undesirable properties related to zero probability estimation both within the observed range of counts and outside into the tails of the distribution. To…
We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium.…
For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are…
In this paper, we present the $\alpha$-$\eta$-$\mathcal{F}$ and $\alpha$-$\kappa$-$\mathcal{F}$ composite fading distributions. The two distributions generalize the two well-known composite fading distributions, namely the…
We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and…
Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…
Algorithms for generating random numbers that follow a gamma distribution with shape parameter less than unity are proposed. Acceptance-rejection algorithms are developed, based on the generalized exponential distribution. The squeeze…
We study a relaxation of the problem of coupling probability distributions -- a list of samples is generated from one distribution and an accept is declared if any one of these samples is identical to the sample generated from the other…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
In the literature different so-called $\kappa$-distribution functions are discussed to fit and model the velocity (or energy) distributions of solar wind species, pickup ions or magnetospheric particles. Here we introduce a generalized…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure…
Many Imitation and Reinforcement Learning approaches rely on the availability of expert-generated demonstrations for learning policies or value functions from data. Obtaining a reliable distribution of trajectories from motion planners is…