广义函数δ（x_1,…,x_（2m））和δ（x_1,…,x_（2m-1））I（x_（2m））的乘积（英文）

AB 用非标准分析和广义函数的调和表示,给出广义函数δ（x_1,…,x_（2m））和δ（x_1,…,x_（2m-1））Ⅰ（x_（2m））的乘积.     

Wavelet modeling of priors on triangles

Parameters in statistical problems often live in a geometry of certain shape. For example, count probabilities in a multinomial distribution belong to a simplex. For these problems, Bayesian analysis needs to model priors satisfying certain constraints imposed by the geometry. This paper investigates modeling of priors on triangles by use of wavelets constructed specifically for triangles. Theoretical analysis and numerical simulations show that our modeling is flexible and is superior to the commonly used Dirichlet prior.     

����Ŀ��ʱ�����ɢPH�ֲ����ʾ

本文研究毁伤目标离散时间的概率分布和PH表示.在射击时间间隔服从离散PH分布的条件下,本文导出了不考虑发现目标因素和考虑该因素二种情况下,毁伤目标时间的离散PH表示与分布.同时,文章用实例说明了求毁伤目标离散时间的PH表示、概率分布和毁伤目标平均离散时间的方法.     

广义函数δ(x1,…,x2m)和δ(x1,…,x2m-1)(○) I(x2m)的乘积

用非标准分析和广义函数的调和表示,给出广义函数δ(x1,···,x2m)和δ(x1,…,x2m-1)(○)I(x2m)的乘积.

Abstract：

In this paper, we get the product of distributions δ(x1,···, x2m) and δ(x1,···, x2m-1)(○)I(x2m), defined by using nonstandard analysis and harmonic representations of distribution.     

A distribution space for Hilbert transform and its applications

In this paper, a new distribution space is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that is the biggest subspace of on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for L ^p functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space are given and a class of useful nonlinear phase signals is shown to be in . Finally, the applications of the extended Hilbert transform are discussed. This work was supported by the National Natural Science Foundation of China (Grant Nos. 60475042, 10631080)     

On a Special Generalized Mixture Class of Probabilistic Models

In this paper, we develop a new mathematical strategy to create flexible lifetime distributions. This strategy is based on a special general-ized mixture derived to the one involved in the so-called weighted exponential distribution. Thus, we introduce a new class of lifetime distributions called "special generalized mixture" class and discussed its qualities. In particular, a short list of new lifetime distributions is presented in details, with a focus on the one based on the Lomax distribution. Different mathematical proper-ties are described, including distributional results, diverse moments measures, incomplete moments, characteristic function and bivariate extensions. Then, the applicability of the new class is investigated through the model parameters based on the Lomax distribution and the analysis of a practical data set.     

Accelerated failure time regression for backward recurrence times and current durations

Backward recurrence times in stationary renewal processes and current durations in dynamic populations observed at a cross-section may yield estimates of underlying interarrival times or survival distributions under suitable stationarity assumptions. Regression models have been proposed for these situations, but accelerated failure time models have the particularly attractive feature that they are preserved when going from the backward recurrence times to the underlying survival distribution of interest. This simple fact has recently been noticed in a sociological context and is here illustrated by a study of current duration of time to pregnancy.     

Expansions and penultimate distributions of maxima of bivariate normal random vectors

It is well known that the marginal maxima of n$n$ standard normal random vectors with correlation coefficient ρ<1$\rho <1$ are asymptotically independent. In this article, the residual dependence will be captured by asymptotic expansions and certain penultimate distributions including the case where ρ(n)↑1$\rho \left(n\right)\uparrow 1$ at a certain rate.     

高维Kramers系统离出点的分布问题

通过对高维Kramers系统与之对应稳态Fokker-Planck方程的渐近分析,仔细探讨了该系统在平衡点吸引域的边界上离出点的分布问题.运用变量替换、匹配原理、局部坐标变换、边界层展开等方法,对外解、远离鞍点处的边界层及鞍点处的边界层进行分析,得出离出点分布的渐近表达式.     

两个矩阵分布的信息特征

熵是一个分布的重要信息特征，通过对矩阵变量积分的一些技巧，利用矩阵r分布的特征，本文获得了矩阵F分布和矩阵Beta分布的熵．     

两个矩阵分布的信息特征

熵是一个分布的重要信息特征,通过对矩阵变量积分的一些技巧,利用矩阵Γ分布的特征,本文获得了矩阵F分布和矩阵Beta分布的熵.     

Involutive Distributions,Invariant Manifolds,and Defining Equations

We introduce the notion of an invariant solution relative to an involutive distribution. We give sufficient conditions for existence of such a solution to a system of differential equations. In the case of an evolution system of partial differential equations we describe how to construct auxiliary equations for functions determining differential constraints compatible with the original system. Using this theorem, we introduce linear and quasilinear defining equations which enable us to find some classes of involutive distributions, nonclassical symmetries, and differential constraints. We present examples of reductions and exact solutions to some partial differential equations stemming from applications.     

A comparison of procedures for estimating the parent probability distribution from a given set of fractiles

On one hand, eliciting subjective probabilities (fractiles) is a well-established procedure. On the other hand, knowledge of a subjective variable's central moments or distribution function is often assumed. However, the problem of converting elicited fractiles into the required moments or distribution function has been largely ignored. We show that this conversion problem is far from trivial, and that the most commonly used conversion procedures often produce huge errors. Alternative procedures are proposed; the “Tocher's curve” and “linear function of fractiles” methods are shown to be much more accurate than the commonly used procedures.     

论文作者数量的统计分析

本文在显著性水平 α=0 .0 1时 ,给出了《应用数学》论文作者数量服从 Lotka分布 f(yx) =0 .81 4 2 /x2 .870 9的结论 ,并对这个结果进行了统计分析 .     

威布尔分布的Bayes可靠性分析

本文针对两参数的威布尔分布的元件，采用Ｂａｙｅｓ方法对其可靠性进行分析，文中分别对两种假设情况进行了讨论，第一种情况是形状参数为离散取值，尺度参数为连续取值的情况，第二种情况假设形状参数的先验分布为均匀分布，尺度参数的先验分布为逆伽玛分布，推出了对应的可靠性估计和置信下限估计，并给出了计算算法，最后用实例对算法进行了验证。     

分层教学的Bayes分析

对学校分层教学进行了初步探索 ,提出了分层分班的 Bayes决策 ,介绍了分层分班方法 ,获得了一些结论 ,并完成了对这些结论的证明 ,从理论上论述了分层教学是实施“因材施教”教育原则和素质教育的有效途径 ,给出了应用实例 .     

Evaluation of Cost Efficiency in Finnish Electricity Distribution

This paper describes the process of developing an approach to evaluating the cost-efficiency of Finnish electricity distribution companies based on Data Envelopment Analysis (DEA). The process consisted of three main stages (1) describing of the problem and exploring the key factors, (2) finding measurable quantities for the most essential factors, and (3) selecting the final model to be used in the regulation. Especially the selection of environmental variables, which allow the comparison of distribution companies operating in different environments, played a key role in the process. The selected model is used as a part of the regulation of distribution pricing.     

An ellipsoidal frontier model: Allocating input via parametric DEA

This paper presents the ellipsoidal frontier model (EFM), a parametric data envelopment analysis (DEA) model for input allocation. EFM addresses the problem of distributing a single total fixed input by assuming the existence of a predefined locus of points that characterizes the DEA frontier. Numeric examples included in the paper show EFM’s capacity to allocate shares of the total fixed input to each DMU so that they will all become efficient. By varying the eccentricities, input distribution can be performed in infinite ways, gaining control over DEA weights assigned to the variables in the model. We also show that EFM assures strong efficiency and behaves coherently within the context of sensitivity analysis, two properties that are not observed in other models found in the technical literature.     

广义函数多目标规划的充分条件

本文借助于广义函数的调和表示，采用非标准分析方法，给出广义函数多目标规划的几个充分条件．