Related papers: New Developments on the Non-Central Chi-Squared an…
Several distributions are studied, simultaneously in the real, complex, quaternion and octonion cases. Specifically, these are the central, nonsingular matricvariate and matrix multivariate T and beta type II distributions and the joint…
One of the distinctive feature of the QCD phase diagram is the possible emergence of a critical endpoint. The critical region around the critical point and the path dependency of the critical exponents is investigated within effective…
We present a characterization of the null moments of the Complex Multivariate Normal Distribution with non-singular covariance matrix and we give closed-forms expressions for its non-null moments.
The properties of the square bias transformation are studied, in particular, the precise moment-type estimate for the $L_1$-metric between the transformed and the original distributions is proved, a relation between their characteristic…
Finite mixtures of regression models provide a flexible modeling framework for many phenomena. Using moment-based estimation of the regression parameters, we develop unbiased estimators with a minimum of assumptions on the mixture…
We develop a family of chiral measures to quantify the chirality of a distribution and assign it a handedness. Our measures are built using the tensorial moments of the distribution, which naturally encode its spatial character, not only…
Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…
In highly nonlinear systems such as the ones commonly found in astrodynamics, Gaussian distributions generally evolve into non-Gaussian distributions. This paper introduces a method for effectively controlling non-Gaussian distributions in…
It is commonly believed that in confining vector-like gauge theories the center and chiral symmetry realizations are parametrically entangled, and if phase transitions occur, they must take place around the strong scale $\Lambda^{-1}$ of…
A new class of nonparametric prior distributions, termed Beta-Binomial stick-breaking process, is proposed. By allowing the underlying length random variables to be dependent through a Beta marginals Markov chain, an appealing discrete…
The piecewise quadratic polynomial collocation is used to approximate the nonlocal model, which generally obtain the {\em nonsymmetric indefinite system} [Chen et al., IMA J. Numer. Anal., (2021)]. In this case, the discrete maximum…
The propagation of an initially localized excitation in one dimensional incommensurate, quasiperiodic and random systems is investigated numerically. It is discovered that the time evolution of variances $\sigma^2(t)$ of atom displacements…
In the vicinity of the onset of an instability, we investigate the effect of colored multiplicative noise on the scaling of the moments of the unstable mode amplitude. We introduce a family of zero dimensional models for which we can…
We present the resolution of a long-standing discrepancy between the moments of parton distributions calculated from lattice QCD and their experimental values. We propose a simple extrapolation formula for the moments of the nonsinglet…
Pearson's chi-squared test, from 1900, is the standard statistical tool for "hypothesis testing on distributions": namely, given samples from an unknown distribution $Q$ that may or may not equal a hypothesis distribution $P$, we want to…
In this paper, we prove a local limit theorem for the chi-square distribution with $r > 0$ degrees of freedom and noncentrality parameter $\lambda \geq 0$. We use it to develop refined normal approximations for the survival function. Our…
This paper studies the nonlinear stochastic partial differential equation of fractional orders both in space and time variables: \[ \left(\partial^\beta+\frac{\nu}{2}(-\Delta)^{\alpha/2}\right)u(t,x) =…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival…
We derive the conjugate prior of the Dirichlet and beta distributions and explore it with numerical examples to gain an intuitive understanding of the distribution itself, its hyperparameters, and conditions concerning its convergence. Due…