Related papers: On the Voigt profile and its dual
Considerable efforts have been devoted to statistical modeling and the characterization of channels in a range of statistical models for fading channels. In this paper, we consider a unified approach to model wireless channels by the…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework,…
We present a method based on unsupervised machine learning to identify regions of interest using particle velocity distributions as a signature pattern. An automatic density estimation technique is applied to particle distributions provided…
Experimental results for the evolution of the probability distribution function (PDF) of a scalar mixed by a turbulence flow in a channel are presented. The sequence of PDF from an initial skewed distribution to a sharp Gaussian is found to…
We study stochastic perturbations of linear systems of the form $$ dv(t)+Av(t)dt = \epsilon P(v(t))dt+\sqrt{\epsilon}B(v(t)) dW (t), v\in\mathbb{R}^{D}, (*) $$ where $A$ is a linear operator with non-zero imaginary spectrum. It is assumed…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
The problem of estimating the L\'evy density of a partially observed multidimensional affine process from low-frequency and mixed-frequency data is considered. The estimation methodology is based on the log-affine representation of the…
A smooth and strictly convex function on an open convex domain induces both (1) a Hessian manifold with respect to the standard flat Euclidean connection, and (2) a dually flat space of information geometry. We first review these…
Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are…
The mean-field theory for two-layer neural networks considers infinitely wide networks that are linearly parameterized by a probability measure over the parameter space. This nonparametric perspective has significantly advanced both the…
Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice…
Numerical simulations of convection in a layer filled with ideal gas are presented. The control parameters are chosen such that there is a significant variation of density of the gas in going from the bottom to the top of the layer. The…
In ref [math.ST/0411462] the notion of statistically dual distributions is introduced. The reconstruction of confidence density [AIP Conference Proceedings 803 (2005) 398] for the location parameter for several pairs of statistically dual…
One aim of data mining is the identification of interesting structures in data. For better analytical results, the basic properties of an empirical distribution, such as skewness and eventual clipping, i.e. hard limits in value ranges, need…
In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of…
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…
We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…
We have measured the local and global statistics of singularity velocity, v, and have related these through the spatial correlation function of v. The distribution of v is a mixture of a mesoscopic distribution of global change in the…