相关论文: Exact Distribution of the Noncentral Complex Roy's…

Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients have combinatorial significance for many classical…

Impropriety testing for complex-valued vector has been considered lately due to potential applications ranging from digital communications to complex media imaging. This paper provides new results for such tests in the asymptotic regime,…

We establish and fully characterize the multidimensional extension of the Stronger Central Sets Theorem. Additionally, we develop a polynomial generalization of this result. Our approach utilizes tools from the Algebra of the Stone-\v{C}ech…

In this paper, we first consider a flat plate (called a lamina) with uniform density $\rho$ that occupies a region $\mathfrak R$ of the plane. We show that the location of the center of mass, also known as the centroid, of the region equals…

This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…

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…

Solving the exact renormalisation group equation a la Wilson-Polchinski perturbatively, we derive a power-counting theorem for general matrix models with arbitrarily non-local propagators. The power-counting degree is determined by two…

The multiplicity distribution of particles in relativistic gases is studied in terms of Tsallis' nonextensive statistics. For an entropic index q>1 the multiplicity distribution is wider than the Poisson distribution with the same average…

Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…

The parton distribution function of the pion in the valence region is extracted in a next-to-leading order analysis from Fermilab E-615 pionic Drell-Yan data. The effects of the parameterization of the pion's valence distributions are…

Recent large scale genome wide association analysis involves large scale linear mixed models. Quantifying (co)-variance parameters in the mixed models with a restricted maximum likelihood method results in a score function which is the…

A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…

We consider random polynomials whose coefficients are independent and identically distributed on the integers. We prove that if the coefficient distribution has bounded support and its probability to take any particular value is at most…

In a thought-provoking paper, Efron (2011) investigated the merit and limitation of an empirical Bayes method to correct selection bias based on Tweedie's formula first reported by \cite{Robbins:1956}. The exceptional virtue of Tweedie's…

We prove that certain natural random variables associated with the local eigenvalue statistics for generalized lattice Anderson models constructed with finite-rank perturbations are compound Poisson distributed. This distribution is…

For every $m\in\mathbb{N}$, we establish the equidistribution of the sequence of the averaged pull-backs of a Dirac measure at any given value in $\mathbb{C}\setminus\{0\}$ under the $m$-th order derivatives of the iterates of a polynomials…

The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…

The average density of zeros for monic generalized polynomials, $P_n(z)=\phi(z)+\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\phi ,f_k$ and real Gaussian coefficients is expressed in terms of correlation functions of the values of the…

We provide a determination of the isotriplet quark distribution from available deep--inelastic data using neural networks. We give a general introduction to the neural network approach to parton distributions, which provides a solution to…

Knowing a sequence of moments of a given, infinitely supported, distribution we obtain quickly: coefficients of the power series expansion of monic polynomials $\left\{ p_{n}\right\} _{n\geq 0}$ that are orthogonal with respect to this…