Related papers: A note on truncated degenerate Bell polynomials
We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables.
A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…
Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures…
In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian…
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…
In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number. In this paper, as natural companions to derangement numbers and degenerate…
In this note, by the umbra calculus method, the Sun and Zagier's congruences involving the Bell numbers and the derangement numbers are generalized to the polynomial cases. Some special congruences are also provided.
We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a…
Completely random measures (CRMs) and their normalizations are a rich source of Bayesian nonparametric priors. Examples include the beta, gamma, and Dirichlet processes. In this paper we detail two major classes of sequential CRM…
In this paper we revisit the work of E.T. Bell concerning partition polynomials in order to introduce the reciprocal partition polynomials. We give their explicit formulas and apply the result to compute closed formulae for some well-known…
In the present article we derive an explicit expression for the trun- cated mean and variance for the multivariate normal distribution with ar- bitrary rectangular double truncation. We use the moment generating ap- proach of Tallis (1961)…
The assumption of a deterministic local hidden variable model constrains the experimentally accessible statistics in a Bell experiment to be contained in the Bell-local polytope. But what if the outputs for only a subset of the measurements…
The finite sensitivity of instruments or detection methods means that data sets in many areas of astronomy, for example cosmological or exoplanet surveys, are necessarily systematically incomplete. Such data sets, where the population being…
In experiment, the multiplicity distributions of inelastic processes are truncated due to finite energy, insufficient statistics or special choice of events. It is shown that the moments of such truncated multiplicity distributions possess…
The aim of this paper is by using generating functions to further study some identities and properties on the degenerate Stirling numbers of the second kind, the degenerate $r$-Stirling numbers of the second kind, the degenerate Stirling…
We introduce a class of sequences, defined by means of partial Bell polynomials, that contains a basis for the space of linear recurrence sequences with constant coefficients as well as other well-known sequences like Catalan and Motzkin.…
This work deals with the estimation of the extreme value index and extreme quantiles for heavy tailed data,randomly right truncated by another heavy tailed variable. Under mild assumptions and the condition thatthe truncated variable is…
Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities; and, the results have been consistent with all measured molecules. However, given that finite-state models result in inconsistencies…
A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Hermite polynomials is proposed, its some properties such as generating…
Spivey's combinatorial method revealed an important identity for Bell numbers, involving Stirling numbers of the second kind. This paper extends his work by deriving Spivey-type recurrence relations for fully degenerate Bell polynomials and…