Related papers: Parameter estimation for kappa distributions using…
Kappa-distributed velocities in plasmas are common in a wide variety of settings, from low-density to high-density plasmas. To date, they have been found mainly in space plasmas, but are recently being considered also in the modelling of…
From the perspective of non-equilibrium statistical mechanics, modeling the velocity distribution of particles in non-equilibrium, steady-state plasmas presents a significant challenge. Under this context, a family of kappa distributions…
The kappa distribution of velocities appears routinely in the study of collisionless plasmas present in Earth's magnetosphere, the solar wind among other contexts where particles are unable to reach thermal equilibrium. Originally justified…
A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization…
The class of $\alpha$-stable distributions with a wide range of applications in economics, telecommunications, biology, applied, and theoretical physics. This is due to the fact that it possesses both the skewness and heavy tails. Since…
The kappa-deformed statistics has been studied in many papers. It is naturally important question for us to ask what should the kappa parameter stand for and under what physical situation should the kappa-deformed statistics be suitable for…
For various plasma applications the so-called (non-relativistic) $\kappa$-distribution is widely used to reproduce and interpret the suprathermal particle populations exhibiting a power-law distribution in velocity or energy. Despite its…
Dramatic increases in the size and dimensionality of many recent data sets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation-maximization…
Expectation maximisation (EM) is an unsupervised learning method for estimating the parameters of a finite mixture distribution. It works by introducing "hidden" or "latent" variables via Baum's auxiliary function $Q$ that allow the joint…
The class of $\alpha$-stable distributions received much interest for modelling impulsive phenomena occur in engineering, economics, insurance, and physics. The lack of non-analytical form for probability density function is considered as…
This paper presents the misestimation of temperature when observations from a kappa distributed plasma are analyzed as a Maxwellian. One common method to calculate the space plasma parameters is by fitting the observed distributions using…
The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…
The standard (non-relativistic) $\kappa$-distribution is widely used to fit data and to describe macroscopic thermodynamical behavior, e.g.\ the pressure (temperature) as the second moment of the distribution function. By contrast to a…
The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…
The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…
The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…
This paper studies sufficient conditions for deriving the kappa distribution in polytropic plasmas by an improved method compared with the previous work [R. Guo, Phys. Plasmas \textbf{27}, 122104 (2020)]. We find that the polytropic…
The Earth's magnetosphere represents a natural plasma laboratory that allows us to study the behavior of particle distribution functions in the absence of Coulomb collisions, typically described by the Kappa distributions. We have…
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…