Moments of Generalized Wishart Distributions

Moments of generalized Wishart distributions are obtained through tensor differential forms and reindexing.     

Operator Semi-Stable Distributions

Abstract

Jajte introduced the operator semi-stable distributions on R ⁿ in [2 Jajte , R. 1977 . Semi-stable probability measures on R ^N . Studia Math. 61 : 29 – 39 . [Google Scholar]] and proved an important fact: A full distribution μ is operator semi-stable, if and only if, there exist a number c(0 < c < 1), a vector h ∈ R ⁿ , and a nonsingular linear operator B in R ⁿ such that the formula μ ^c  = Bμ*δ(h) holds. In this paper, we make use of the eigenvalue of the matrix B to give a necessary and sufficient condition for ∫_|x|≤1|x| ^r M(dx) < ∞, where M is the Lévy measure of μ. Also, we use the symmetric group of μ to characterize the operators B in (1).     

Multivariate Discrete Distributions with a Product-Type Dependence

A discrete multivariate probability distribution for dependent random variables, which contains the Poisson and Geometric conditionals distributions as particular cases, is characterized by means of conditional expectations of arbitrary one-to-one functions. Independence of the random variables is also characterized in terms of these conditional expectations. For certain exchangeable and partially exchangeable random variables with a joint distribution of this form it is shown that maximum likelihood estimates coincide with the simple method of moments estimates, suggesting that these models offer a pragmatic way to analyze certain dependent data.     

Factorial Moments of Distributions of Additive Functions

We study the weak convergence of the distribution functions

多个离散分布的信息差度量的渐近分布

本文中对于多信息源的信息差异性度量B,我们研究了B(u1,u2,…,us)的渐近分布,其中u1,u2,…us是某个概率分布的样本估计．在某些较弱的条件下,我们证明了nB(u1,u2,…,us)的极限分布是自由度为1的X2分布的加权和,其中n是样本容量,u1,u2,…,us不必相互独立．     

Discrete Tempered Stable Distributions

Methodology and Computing in Applied Probability - Discrete tempered stable distributions are a large and flexible class of models for heavy tailed and overdispersed count data. In this paper we...     

离散分数阶和分算子与差分算子及互逆性

对连续函数进行离散化,给出离散序列的分数阶和分算子与分数阶差分算子的解析表达式,证明了两算子满足交换律、指数率与互逆性.     

The Inverse Problem for a Discrete Periodic Schrodinger Operator

We study isospectral sets for a discrete 1D Schrodinger operator on ℤ with an (N + 1)-periodic potential. We show that for small odd potentials, the isospectral set consists of 2^{(N + 1)/2} elements, while for large potentials, the isospectral set consists of (N +1)! elements. Moreover, asymptotics for endpoints of the spectrum of the Schrodinger operator for small (and large) potentials are determined. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 315, 2004, pp. 96–101.     

On Moments of Folded and Truncated Multivariate Normal Distributions

Recurrence relations for integrals that involve the density of multivariate normal distributions are developed. These recursions allow fast computation of the moments of folded and truncated multivariate normal distributions. Besides being numerically efficient, the proposed recursions also allow us to obtain explicit expressions of low-order moments of folded and truncated multivariate normal distributions. Supplementary material for this article is available online.     

一类系数中含有指数函数和幂函数的J-自伴微分算子谱的离散性

运用算子直和分解法和二次型比较法研究了由2n阶复系数中含有指数函数和幂函数的微分算式所生成的J-自伴微分算子谱的离散性,得到了一类系数中含有指数函数和幂函数的J-自伴微分算子谱是离散的若干充分条件.     

Parameter Estimation of Discrete Multivariate Phase-Type Distributions

This paper considers parameter estimation of a class of discrete multi-variate phase-type distributions (DMPH). Such discrete phase-type distributions are based on discrete Markov chains with marked transitions introduced by He and Neuts (Stoch Process Appl 74(1):37–52, 1998) and is a generalization of the discrete univariate phase–type distributions. Properties of the DMPHs are presented. An EM-algorithm is developed for estimating the parameters for DMPHs. A number of numerical examples are provided to address some interesting parameter selection issues and to show possible applications of DMPHs.     

Root System of a Perturbation of a Selfadjoint Operator with Discrete Spectrum

We analyze the perturbations T?+?B of a selfadjoint operator T in a Hilbert space H with discrete spectrum ${\{ t_k\}, T \phi_k = t_k \phi_k}$ . In particular, if t _k+1 ? t _k ?? ck ^{?? - 1}, ?? > 1/2 and ${\| B \phi_k \| = o(k^{\alpha - 1})}$ then the system of root vectors of T?+?B, eventually eigenvectors of geometric multiplicity 1, is an unconditional basis in H (Theorem 6). Under the assumptions ${t_{k+p} - t_k \geq d > 0, \forall k}$ (with d and p fixed) and ${\| B \phi_k \| \rightarrow 0}$ a Riesz system {P _k } of projections on invariant subspaces of T?+?B, Rank P _k ?? p, is constructed (Theorem 3).     

Discrete Spectrum of a Three-Particle Schrodinger Operator with a Homogeneous Magnetic Field

The discrete spectrum of the Schrödinger operator is studiedfor a system of three identical particles with short-range interactionsin a homogeneous magnetic field. All the two-particle subsystemsare supposed to be unstable. Finiteness of the discrete spectrumis established under some assumptions about the solutions ofthe corresponding two-particle Schrödinger equation.     

MM Algorithms for Some Discrete Multivariate Distributions

The MM (minorization–maximization) principle is a versatile tool for constructing optimization algorithms. Every EM algorithm is an MM algorithm but not vice versa. This article derives MM algorithms for maximum likelihood estimation with discrete multivariate distributions such as the Dirichlet-multinomial and Connor–Mosimann distributions, the Neerchal–Morel distribution, the negative-multinomial distribution, certain distributions on partitions, and zero-truncated and zero-inflated distributions. These MM algorithms increase the likelihood at each iteration and reliably converge to the maximum from well-chosen initial values. Because they involve no matrix inversion, the algorithms are especially pertinent to high-dimensional problems. To illustrate the performance of the MM algorithms, we compare them to Newton’s method on data used to classify handwritten digits.     

A Discrete Model for the Bi-Carleson Operator

We prove L^p estimates for the Walsh model of the maximal bi-Carleson operator defined below. The corresponding estimates for the Fourier model will be obtained in the sequel [MTT4] of this paper.