In this paper, we introduce a bivariate Kantorovich variant of combination of Szász and Chlodowsky operators based on Charlier polynomials. Then, we study local approximation properties for these operators. Also, we estimate the approximation order in terms of Peetre's K-functional and partial moduli of continuity. Furthermore, we introduce the associated GBS-case (Generalized Boolean Sum) of t...

The possibility of reliable monitoring processes occurring near the ocean-atmosphere boundary is determined by how fully and correctly geometric structure sea surface described. paper analyzes possibilities approximating probability density function (PDF) elevations truncated Edgeworth series. increasing truncation order using a regression equation linking third fifth statistical moments consid...

Abstract. We consider free multiple stochastic measures in the combinatorial framework of the lattice of all diagonals of an n-dimensional space. In this free case, one can restrict the analysis to only the noncrossing diagonals. We give definitions of what free multiple stochastic measures are, and calculate them for the free Poisson and free compound Poisson processes. We also derive general ...

The paper devises a family of leptokurtic bell-shaped distributions which is based on the hyperbolic secant raised to a positive power, and bridges the Laplace and Gaussian laws on asymptotic arguments. Moment and cumulant generating functions are then derived and represented in terms of polygamma functions. The behaviour of shape parameters, namely kurtosis and entropy, is investigated. In add...

Starting from the D!-Riccati Diierence equation satissed by the Stieltjes function of a linear functional, we work out an algorithm which enables us to write the general fourth-order diierence equation satissed by the associated of any integer order of orthogonal polynomials of the-Laguerre-Hahn class. Moreover, in classical situations (Meixner, Charlier, Krawtchouk and Hahn), we give these dii...