相关论文: Generalized Stieltjes Transforms of Compactly-Supp…

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…

Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…

In this paper we study a wide and flexible family of discrete distributions, the so-called generalized negative binomial (GNB) distributions that are mixed Poisson distributions in which the mixing laws belong to the class of generalized…

The Schl\"omilch integral, a generalization of the Dirichlet integral on the simplex, and related probability distributions are reviewed. A distribution that unifies several generalizations of the Dirichlet distribution is presented, with…

Here we consider the degenerate Bernstein polynomials as a degenerate version of Bernstein polynomials, which are motivated by Simsek's recent work 'Generating functions for unification of the multidimensional Bernstein polynomials and…

We generalise the known fact that for binomial $X_{n,k} \sim \mathrm{Bin}(n, k/n)$ one has $\inf_{k>1,n} \mathrm{P}(X_{n,k} \geq k) \geq \lim_{k \to 1+}\mathrm{P}(X_{2,k} \geq k) = 1/4$ to cover probabilities of exceeding a constant shift…

We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing…

Random integers, sampled uniformly from $[1,x]$, share similarities with random permutations, sampled uniformly from $S_n$. These similarities include the Erd\H{o}s--Kac theorem on the distribution of the number of prime factors of a random…

In this paper, we investigate fractional B splines and their connections with Fourier analysis, and establish connections with generalized Stirling-type numbers and distribution theory. Employing a generating function approach inspired by…

The Poisson-binomial distribution is useful in many applied problems in engineering, actuarial science, and data mining. The Poisson-binomial distribution models the distribution of the sum of independent but not identically distributed…

Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…

We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the $j^{th}$ derivatives of a sequence generating…

The resummation of superfactorially divergent series represents a significant computational challenge in mathematical physics. In the present paper the resummation of a specific class of Stieltjes series characterized by a moment sequence…

We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is computed. The distribution function is…

We establish some identities in law for the convolution of a beta prime distribution with itself, involving the square root of beta distributions. The proof of these identities relies on transformations on generalized hypergeometric series…

We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and…

A transformation group approach to the prior for the parameters of the beta distribution is suggested which accounts for finite sets of data by imposing a limit to the range of parameter values under consideration. The relationship between…

We introduce and study a subclass of joint Bernoulli distributions which has the palindromic property. For such distributions the vector of joint probabilities is unchanged when the order of the elements is reversed. We prove for binary…

We introduce a theory of probability in $\lambda$-rings designed to efficiently describe random variables valued in multisets of complex numbers, varieties over a field, or other similar enriched settings. A key role is played by the…

We develop series representations for the Hurwitz and Riemann zeta functions in terms of generalized Bernoulli numbers (N\"{o}rlund polynomials), that give the analytic continuation of these functions to the entire complex plane. Special…