相关论文: Beta distribution and associated Stirling numbers …
We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…
Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…
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 the paper, the author finds an explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind.
In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here the related special numbers are Stirling numbers of the…
We present new proofs for some summation identities involving Stirling numbers of both first and second kind. The two main identities show a connection between Stirling numbers and Bessel numbers. Our method is based on solving a particular…
Recently, several authors have studied the Stirling numbers of the second kind and Bell polynomials. In this paper, we study the extended Stirling polynomials of the second kind and the extended Bell polynomials associated with the Stirling…
We give explicit estimates for the Stirling numbers of the second kind $S(n,m)$. With a few exceptions, such estimates are asymptotically sharp. The form of these estimates varies according to $m$ lying in the central or non-central regions…
In the note, the author discovers an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.
The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two…
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…
In this present paper, we show that the Stirling numbers of the first kind with higher level connected with the probability distribution of the number of records and record times in the so-called F^{\alpha}-scheme. In addition, we determine…
We introduce the $B$-Stirling numbers of the first and second kind, which are the coefficients of the potential polynomials when we express them in terms of the monomials and the falling factorials, respectively. These numbers include, as…
In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.
This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.
This paper investigates the Stirling numbers of the first and second kind associated with a delta series f (t). These numbers provide a robust framework that satisfies the orthogonality and inverse relations, often lacking in recent…
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…
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. Recently, probabilistic Stirling numbers of the first kind and of the second kind associated with Y have been introduced. However,…
This paper considers the issue of modeling fractional data observed in the interval [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are proposed. The beta distribution is used to describe the continuous component of the model…
The most well known probability distribution of probabilities is the Beta distribution. If we have observed $r$ `successes', each having a probability $\theta$, and $n-r$ `failures', each having a probability $1-\theta$. In this paper we…