Related papers: Comment: Gibbs Sampling, Exponential Families, and…
Sequences of orthogonal polynomials that are alternative to the Jacobi polynomials on the interval $[0,1]$ are defined and their properties are established. An $(\alpha,\beta)$-parameterized system of orthogonal polynomials of the…
This paper introduces a notion of 2-orthogonality for a sequence of polynomials to give extended versions of the Meixner and Feinsilver characterization results based on orthogonal polynomials. These new versions subsume the Letac-Mora…
Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which…
Preliminary version of Chapter 2 in the book "Encyclopedia of Special functions: The Askey-Bateman Project, Vol. 2: Multivariate special functions", T. H. Koornwinder and J. V. Stokman (eds.), Cambridge University Press, 2021.
In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…
In this paper we focus on two new families of polynomials which are connected with exponential polynomials and geometric polynomials. We discuss their generalizations and show that these new families of polynomials and their generalizations…
We introduce a new family of multiple orthogonal polynomials satisfying orthogonality conditions with respect to two weights $(w_1,w_2)$ on the positive real line, with $w_1(x)=x^\alpha e^{-x}$ the gamma density and $w_2(x) = x^\alpha…
We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain…
In the 6th Int. Symposium on OPSFA there were several communications dealing with concrete applications of orthogonal polynomials to experimental and theoretical physics, chemistry, biology and statistics. Here I make suggestions concerning…
In this notice, we revisit the recent work [1] of Jung Yoog Kang and Tai Sup about special polynomials with exponential distribution in order to state some improvements and get new proofs for results therein.
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…
We give a survey of the analytic theory of matrix orthogonal polynomials.
We review the properties of six families of orthogonal polynomials that form the main bulk of the collection called the Askey--Wilson scheme of polynomials. We give connection coefficients between them as well as the so-called linearization…
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
An observation on Hall-Littlewood polynomials.
A new class of distributions, called Generalized One Parameter Polynomial Exponential-G family of distributions is proposed for modelling lifetime data. An account of the structural and reliability properties of the new class is presented.…
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
Rejoinder of "Instrumental Variables: An Econometrician's Perspective" by Guido W. Imbens [arXiv:1410.0163].
Recently, a very attractive logistic regression inference method for exponential family Gibbs spatial point processes was introduced. We combined it with the technique of quadratic tangential variational approximation and derived a new…