Related papers: New Results On the Sum of Two Generalized Gaussian…
We obtain generalized Christoffel-Darboux (GCD) formula for skew-orthogonal polynomials (SOP). Using this, we present an alternative derivation of the level density and two-point function for Gaussian orthogonal ensembles (GOE) and Gaussian…
We study the probability distribution $F(u)$ of the maximum of smooth Gaussian fields defined on compact subsets of $\R^d$ having some geometric regularity. Our main result is a general formula for the density of $F$. Even though this is an…
The statistical distribution of the ratio of two normal random variables is characterized by its heavy-tailed nature and absence of finite moments. The shape of its density function is highly variable, capable of exhibiting unimodal or…
The spectral form factor (SFF) plays a crucial role in revealing the statistical properties of energy level distributions in complex systems. It is one of the tools to diagnose quantum chaos and unravel the universal dynamics therein. The…
We have investigated a weighted chi-square distribution of the variable $\xi$ which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles $\phi_k=2\pi k/N$, where $k \in \{0,1,...,N-1\}$…
We derive the exact probability density function of the product of $N$ independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and…
In this paper, we investigate the convergence properties of Fourier partial sums associated with general orthonormal systems, focusing on functions that belong to specific differentiable function classes. While classical Fourier analysis…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
The present work proposes analytical solutions for the integral of bivariate Fox H-function in combination with algebraic, exponential, and complementary error functions. In addition, the work also presents the derivative identities with…
This paper introduces max-characteristic functions (max-CFs), which are an offspring of multivariate extreme-value theory. A max-CF characterizes the distribution of a random vector in R^d , whose components are nonnegative and have finite…
The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and…
Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such…
This work examines the problem of using finite Gaussian mixtures (GM) probability density functions in recursive Bayesian peer-to-peer decentralized data fusion (DDF). It is shown that algorithms for both exact and approximate GM DDF lead…
We propose a new generator for the generalized inverse Gaussian (GIG) distribution by decomposing the density of GIG into two components. The first component is a truncated inverse Gamma density, in order to sample from which we improve the…
The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the…
We consider two random variables $X$ and $Y$ following correlated Gamma distributions, characterized by identical scale and shape parameters and a linear correlation coefficient $\rho$. Our focus is on the parameter: \[ D(X,Y) = \frac{|X -…
In this paper, we obtain various series and asymptotic expansions involving the modified Bessel function of the second kind for the normal inverse Gaussian cumulative distribution function. The new expansions accelerate computations,…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
In this paper we present a generalization of the Fox H-function called Fox-Barnes J-function. Like the Fox H-function, it is defined as a contour integral in the complex plane, but instead of an integrand given by a ratio of products of…
An elementary approach is shown which derives the value of the Gauss sum of a cubic character over a finite field $\mathbb F_{2^s}$ without using Davenport-Hasse's theorem (namely, if $s$ is odd the Gauss sum is -1, and if $s$ is even its…