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Normal variance mixtures are a class of multivariate distributions that generalize the multivariate normal by randomizing (or mixing) the covariance matrix via multiplication by a non-negative random variable W. The multivariate t…

Computation · Statistics 2020-06-16 Erik Hintz , Marius Hofert , Christiane Lemieux

We present a probabilistic model for natural images which is based on Gaussian scale mixtures and a simple multiscale representation. In contrast to the dominant approach to modeling whole images focusing on Markov random fields, we…

Machine Learning · Statistics 2012-09-17 Lucas Theis , Reshad Hosseini , Matthias Bethge

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…

Computation · Statistics 2020-05-07 Yuan Fang , Dimitris Karlis , Sanjeena Subedi

An important application of Lebesgue integral quadrature arXiv:1807.06007 is developed. Given two random processes, $f(x)$ and $g(x)$, two generalized eigenvalue problems can be formulated and solved. In addition to obtaining two Lebesgue…

Numerical Analysis · Mathematics 2020-12-01 Vladislav Gennadievich Malyshkin

Let $(X\_1,\ldots,X\_n)$ be a $d$-dimensional i.i.d sample from a distribution with density $f$. The problem of detection of a two-component mixture is considered. Our aim is to decide whether $f$ is the density of a standard Gaussian…

Statistics Theory · Mathematics 2015-10-01 Béatrice Laurent , Clément Marteau , Cathy Maugis-Rabusseau

This paper uses sample data to study the problem of comparing populations on finite-dimensional parallelizable Riemannian manifolds and more general trivial vector bundles. Utilizing triviality, our framework represents populations as…

Methodology · Statistics 2023-11-29 Michael Wilson , Tom Needham , Chiwoo Park , Suprateek Kundu , Anuj Srivastava

This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…

Methodology · Statistics 2019-05-07 Shyamalendu Sinha , Jeffrey D. Hart

There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…

Methodology · Statistics 2018-05-10 Antonio Canale , Daniele Durante , David Dunson

Evaluation of the Voigt function, a convolution of a Lorentzian and a Gaussian profile, is essential in various fields such as spectroscopy, atmospheric science, and astrophysics. Efficient computation of the function is crucial, especially…

Instrumentation and Methods for Astrophysics · Physics 2024-11-05 Mofreh R. Zaghloul , Jacques Le Bourlot

The massive exploitation of cosmic voids for precision cosmology in the upcoming dark energy experiments, requires a robust understanding of their internal structure, particularly of their density profile. We show that the void density…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-18 E. Ricciardelli , V. Quilis , J. Varela

The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centred on lattice sites or via a Fourier sum. Here, we argue that representing instead the $\mathit{logarithm}$ of the density…

Soft Condensed Matter · Physics 2021-06-02 Priya Subramanian , Daniel J. Ratliff , Alastair M. Rucklidge , Andrew J. Archer

CConsider a bipartite quantum system consisting of two subsystems A and B. The reduced density matrix ofA a is obtained by taking the partial trace with respect to B. In this work, we will show that the Wigner distribution of this reduced…

Quantum Physics · Physics 2022-11-17 Maurice de Gosson , Charlyne de Gosson

Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…

Methodology · Statistics 2019-12-30 Luca Scrucca

Let $\bf{x}$ be a random variable with density $\rho(x)$ taking values in ${\mathbb R}^d$. We are interested in finding a representation for the shape of $\rho(x)$, i.e. for the orbit $\{ \rho(g\cdot x) | g\in E(d) \}$ of $\rho$ under the…

Probability · Mathematics 2021-11-23 Mireille Boutin , Kindyl King , Uli Walther

This paper explores mixture distributions induced by a product of the positive stable random variable and a power of another positive random variable. The paper also considers the convolution of the stable density with a gamma density.…

Probability · Mathematics 2025-07-10 Nomvelo Karabo Sibisi

The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In addition to its applications in…

Computation · Statistics 2025-01-28 Victor Peña , Michael Jauch

This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact…

Machine Learning · Computer Science 2022-02-21 Adam Celarek , Pedro Hermosilla , Bernhard Kerbl , Timo Ropinski , Michael Wimmer

A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures…

Probability · Mathematics 2019-04-18 Alexandros Eskenazis , Piotr Nayar , Tomasz Tkocz

This paper proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector…

Statistics Theory · Mathematics 2023-02-28 Tong Pu , Yiying Zhang , Chuancun Yin

Geo-materials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores, which is commonly referred to as double porosity. To…

Fluid Dynamics · Physics 2018-03-07 K. B. Nakshatrala , S. H. S. Joodat , R. Ballarini