Related papers: On Numerical Estimation of Joint Probability Distr…
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We study the utility of Expectation Propagation (EP) as an approximate…
In this paper, we derive a joint central limit theorem for random vector whose components are function of random sesquilinear forms. This result is a natural extension of the existing central limit theory on random quadratic forms. We also…
The g-and-k and (generalised) g-and-h distributions are flexible univariate distributions which can model highly skewed or heavy tailed data through only four parameters: location and scale, and two shape parameters influencing the skewness…
arXiv:2206.10812v1 [stat.ME] proposes a useful algorithm, named generalized Diversity Subsampling (g-DS) algorithm, to select a subsample following some target probability distribution from a finite data set and demonstrates its…
The Voigt profile is the density obtained from the convolution of a Gaussian and a Cauchy and it is widely used in atomic and molecular spectroscopy. We show that the Voigt profile is a scale mixture of Gaussian distributions, with mixing…
This paper combines probability theory and fractional calculus to derive a novel integral representation of the three-parameter Mittag-Leffler function or Prabhakar function, where the three parameters are combinations of four base…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
The proportion of false null hypotheses is a very important quantity in statistical modelling and inference based on the two-component mixture model and its extensions, and in control and estimation of the false discovery rate and false…
Joint distribution function of N eigenvalues of U(N) invariant random-matrix ensemble can be interpreted as a probability density to find N fictitious non-interacting fermions to be confined in a one-dimensional space. Within this picture a…
We study the approximation of expectations $\E(f(X))$ for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms,…
We show that the functional renormalization group (FRG) allows for the calculation of the probability distribution function of the sum of strongly correlated random variables. On the example of the three-dimensional Ising model at…
We trace a conceptual genealogy from Abraham de Moivre's derivation of the normal curve (1733) to the modern distributional approach to statistics. De Moivre's Approximatio ad Summam Terminorum Binomii gave the first systematic derivation…
We analyse correspondence of a text to a simple probabilistic model. The model assumes that the words are selected independently from an infinite dictionary. The probability distribution correspond to the Zipf---Mandelbrot law. We count…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…
Inspired by the theory of quantum information, I use two non-Hermitian random matrix models - a weighted sum of circular unitary ensembles and a product of rectangular Ginibre unitary ensembles - as building blocks of three new products of…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence…
The univariate generalized extreme value (GEV) distribution is the most commonly used tool for analyzing the properties of rare events. The ever greater utilization of Bayesian methods for extreme value analysis warrants detailed…
The Gaussian and Laguerre orthogonal ensembles are fundamental to random matrix theory, and the marginal eigenvalue distributions are basic observable quantities. Notwithstanding a long history, a formulation providing high precision…