Related papers: Comment: Gibbs Sampling, Exponential Families, and…
Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an…
In this paper we use computational method based on operational point of view to prove a new generating function of exponential polynomials. We give its applications involving geometric polynomials, Bernoulli and Euler numbers.
The idea of orthogonal polynomials has been generalized in two ways to achieve new types of polynomials: noncommutative orthogonal polynomials and biorthogonal polynomials. This paper brings these two different generalizations together to…
An open problem about two new families of orthogonal polynomials was posed by Alhaidari. Here we will identify one of them as Wilson polynomials. The other family seems to be new but we show that they are discrete orthogonal polynomials on…
In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.
This article presents and reviews several basic properties of the Cumulative Ord family of distributions; this family contains all the commonly used discrete distributions. A complete classification of the Ord family of probability mass…
We investigate the zonal polynomials, a family of symmetric polynomials that appear in many mathematical contexts, such as multivariate statistics, differential geometry, representation theory, and combinatorics. We present two computer…
Comment on "Biases in the Quasar Mass-Luminosity Plane"
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…
New sequences of orthogonal polynomials with ultra-exponential weight functions are discovered. In particular, it gives an explicit solution to the Ditkin-Prudnikov problem (1966). The 3-term recurrence relations, explicit representations,…
Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems…
We study the distribution of the extended binomial coefficients by deriving a complete asymptotic expansion with uniform error terms. We obtain the expansion from a local central limit theorem and we state all coefficients explicitly as…
The so-called exceptional orthogonal X1-polynomials arise as eigen functions of a Sturm-Liouville problem. In this paper, a generic classification of these polynomials is presented based on Pearson distributions family. Then, six special…
In this paper we describe how MAP inference can be used to sample efficiently from Gibbs distributions. Specifically, we provide means for drawing either approximate or unbiased samples from Gibbs' distributions by introducing low…
In this contribution, discrete semiclassical orthogonal polynomials of class $s\leq2$ are studied. By considering all possible solutions of the Pearson equation, we obtain the canonical families in each class. We also consider limit…
In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization involves the construction of uncountable…
In this paper Fourier transform of multivariate orthogonal polynomials on the simplex is presented. A new family of multivariate orthogonal functions is obtained by using the Parseval's identity and several recurrence relations are derived.
This is a comment on the paper arXiv:1410.2840 by Ji and Jin, to appear in the AOAS.
This paper is devoted to several new results concerning (standard) octonion polynomials. The first is the determination of the roots of all right scalar multiples of octonion polynomials. The roots of left multiples are also discussed,…
A new recurrence relation for exceptional orthogonal polynomials is proposed, which holds for type 1, 2 and 3. As concrete examples, the recurrence relations are given for Xj-Hermite, Laguerre and Jacobi polynomials in j = 1,2 case.