Related papers: Distributional transformations, orthogonal polynom…
We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series…
Let R and S be two irreducible root systems spanning the same vector space and having the same Weyl group W, such that S (but not necessarily R) is reduced. For each such pair (R,S) we construct a family of W-invariant orthogonal…
Orthogonal polynomials with respect to a weight function defined on a wedge in the plane are studied. A basis of orthogonal polynomials is explicitly constructed for two large class of weight functions and the convergence of Fourier…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…
We study arithmetic distribution relations and the inverse function theorem in algebraic and arithmetic geometry, with an emphasis on versions that can be applied uniformly across families of varieties and maps. In particular, we prove two…
We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…
We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a…
In this paper we obtain a set of polynomials which are orthogonal with respect to the classical discrete weight function of the Charlier polynomials at which an extra point mass at x=0 is added. We construct a difference operator of…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
We introduce the notion of the descent set polynomial as an alternative way of encoding the sizes of descent classes of permutations. Descent set polynomials exhibit interesting factorization patterns. We explore the question of when…
We introduce a new family of orthogonal polynomials on the disk that has emerged in the context of wave propagation in layered media. Unlike known examples, the polynomials are orthogonal with respect to a measure all of whose even moments…
In observational causal inference, in order to emulate a randomized experiment, weights are used to render treatments independent of observed covariates. This property is known as balance; in its absence, estimated causal effects may be…
We study skew-orthogonal polynomials with respect to the weight function $\exp[-2V(x)]$, with $V(x)=\sum_{K=1}^{2d}(u_{K}/{K})x^{K}$, $u_{2d} > 0$, $d > 0$. A finite subsequence of such skew-orthogonal polynomials arising in the study of…
We study the convergence of distributions on finite paths of weighted digraphs, namely the family of Boltzmann distributions and the sequence of uniform distributions. Targeting applications to the convergence of distributions on paths, we…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and colored permutations. The corresponding…