反冲塞效应的热弹性理论分析（I）—温度场分析

本对我们新近发现的长脉冲激光束对金属薄片材料的一种新的破坏方式－“反冲塞”效应进行了温度场分析，用Ｈａｎｋｅｌ变换和Ｌａｐｌａｃｅ变换，得到了温度场的精确解，以激光束的空间分布为均匀分布和高斯分布为例对温度场进行了计算，结果表明激光束的空间均匀分布是产生反冲塞效应的主要原因。     

简单混合三参数一般均匀分布在地震发生间隔区间估计中的应用

本文首次介绍了一类一般均匀分布,包括单参数一般均匀分布、二参数一般均匀分布及三参数一般均匀分布,导出了三参数一般均匀分布的密度函数、数学期望、矩母函数及特征函数,获得了单参数及二参数一般均匀分布参数的矩估计和最大似然估计,通过结合最大似然估计法与矩估计法,从而获得了三参数一般均匀分布参数的二种最大似然型修正估计.文末,提出一个简单混合三参数一般均匀分布拟合地震发生时间间隔长度数据,用以预报一段时间内地震发生的概率.     

随机利率下的增额寿险

寿险中的利率随机性问题，是近年来保险精算研完的热点之一，本文以即时给付的毒额寿险为对象，对随机利率采用Gauss过程建模，研究给付现值及其各阶矩，并在死亡均匀分布假设下得到矩的简洁表达式。     

在定数截尾样本下三参数威布尔分布的矩估计

本文讨论了在定数截尾样本下三参数威布尔分布的矩估计问题．在定数截尾情形下，将威布尔分布数据转化为均匀分布数据，利用平均剩余寿命构造样本矩，同时，第三阶矩方程用样本的第一个次序统计量来代替，得到了在定数截尾样本下三参数威布尔分布的矩估计方程，用随机模拟方法得出了矩估计的偏性和均方误差．并与近似MLE进行了比较，表明此矩估计方法有较好的性质．     

有限个均匀分布随机变量之和的分布

<正> 均匀分布是一种最简单而又较常见的分布,有着较广的应用.本文讨论在任意一个区间中有限个相互独立均匀分布的随机变量之和的分布问题. 首先讨论均匀分布的区间长度相等的情况. 设η_1,η_2,…η_n是在区间(0,1)中n个相互独立的均匀分布的随机变量,令η=η_1+     

对于双未知参数均匀分布的序贯 minimax 估计

统计判决理论的一个重要问题,是对一个给定的分布族,当观测是独立同分布的,作n 次观测的费用为 cn(c>0)时,求其参数的序贯 minimax 估计.关于这一问题,Wald对损失函数 W(θ,d)=(θ-d)~2,得到了从 θ-1/2到 θ+1/2(-∞<θ<∞)上的均匀分布中均值θ的估计.Blyth将 Wald 的结果作了推广和改进.Kiefer 关于损失函数 W(θ,d)=[(θ-d)/θ]~2,解决了从0到 θ(0<θ<∞)上的均匀分布中参数θ的估计问题.本文所要讨论的是含有两个未知参数的均匀分布,其密度为     

圆内二维均匀分布的参数估计

研究了圆内二维均匀分布的参数估计,利用次序统计量得到了圆的半径的估计量与置信区间.     

长方体上均匀分布的密度函数

讨论了长方体上均匀分布密度函数问题,得到了长方体体积的估计量、估计量的点估计及估计量的密度函数.     

球面均匀分布的拟合优度检验

证明了基于惯量矩的d维单位球面上样本服从均匀分布的基本特征,得到球面均匀分布协差阵特征根估计的强相合性及渐近多元正态性.提出了检验球面上样本均匀性的渐近卡方统计量,证明了拟合优度检验的相合性并做检验功效的随机模拟.     

慢延伸指数函数中一个序列的理论分布测度

慢延伸指数函数的分项部分的序列是”理想”均匀分布的 .本文对这种”理想”均匀分布的偏离程度给出了一个数值估计 ,并把这一数值估计称为这个序列的理论分布测度 .     

On concentration of measure on the cube

Concentration property of the uniform distribution on the cube is considered for the class of permutation invariant sets. Bibliography: 10 titles.     

Chaos optimization algorithms based on chaotic maps with different probability distribution and search speed for global optimization

Chaos optimization algorithms (COAs) usually utilize the chaotic map like Logistic map to generate the pseudo-random numbers mapped as the design variables for global optimization. Many existing researches indicated that COA can more easily escape from the local minima than classical stochastic optimization algorithms. This paper reveals the inherent mechanism of high efficiency and superior performance of COA, from a new perspective of both the probability distribution property and search speed of chaotic sequences generated by different chaotic maps. The statistical property and search speed of chaotic sequences are represented by the probability density function (PDF) and the Lyapunov exponent, respectively. Meanwhile, the computational performances of hybrid chaos-BFGS algorithms based on eight one-dimensional chaotic maps with different PDF and Lyapunov exponents are compared, in which BFGS is a quasi-Newton method for local optimization. Moreover, several multimodal benchmark examples illustrate that, the probability distribution property and search speed of chaotic sequences from different chaotic maps significantly affect the global searching capability and optimization efficiency of COA. To achieve the high efficiency of COA, it is recommended to adopt the appropriate chaotic map generating the desired chaotic sequences with uniform or nearly uniform probability distribution and large Lyapunov exponent.     

Characterizations of symmetric distributions based on Rényi entropy

It is proved that the equality of Rényi entropies of upper and lower order statistics as well as upper and lower k-records is a characteristic property of symmetric distributions. Also, for Farlie-Gumbel-Morgenstern (FGM) family, it is shown that under some conditions the equality of entropies of concomitants of upper and lower order statistics as well as concomitants of upper and lower record values is a characteristic property for the uniform distribution.     

Propriety of posterior distribution for dichotomous quantal response models

In this article, we investigate the property of posterior distribution for dichotomous quantal response models using a uniform prior distribution on the regression parameters. Sufficient and necessary conditions for the propriety of the posterior distribution with a general link function are established. In addition, the sufficient conditions for the existence of the posterior moments and the posterior moment generating function are also obtained. Finally, the relationship between the propriety of posterior distribution and the existence of the maximum likelihood estimate is examined.

     

Singularity of distributions of random variables given by distributions of elements of the corresponding continued fraction

The structure of the distribution of a random variable for which elements of the corresponding elementary continued fraction are independent random variables is completely studied. We prove that the distribution is pure and the absolute continuity is impossible, give a criterion of singularity, and study the properties of the spectrum. For the distribution of a random variable for which elements of the corresponding continued fraction form a uniform Markov chain, we describe the spectrum, obtain formulas for the distribution function and density, give a criterion of the Cantor property, and prove that an absolutely continuous component is absent.     

A simple characterization of almost uniform convergence by stochastic convergence

Motivated by Egorov's theorem and the characterization of the equivalence of P-stochastic convergence and P-almost convergence by the property of the probability distribution P to be purely atomic and concentrated on a countable number of pairwise disjoint P-atoms (cf. [1], p. 68), it is proved that P-stochastic resp. P-almost convergence is equivalent to P-almost uniform convergence (cf. [2], p. 89/90) if and only if P is purely atomic and concentrated on a finite number of pairwise disjoint P-atoms. Furthermore, this property of P is equivalent to the condition that any P-stochastic convergent sequence admits a P-almost uniform convergent subsequence. Finally a proof is given that P is purely atomic and concentrated on a finite number of pairwise disjoint P-atoms if and only if there does not exist a purely finitely additive {0,1}-valued probability charge, which vanishes for all P-zero sets.     

Almost Uniform Distribution Modulo 1 and the Distribution of Primes

Let (an), n = 1, 2, ... be a sequence of real numbers which is related with number theoretic functions such as Pn, the n-th prime. We study the distribution of the fractional parts of (an) using the concept of "almost uniform distribution" defined in [9]. Then we can show a generalization of the results of [2] on the convex property of log Pn. The method may be extended as well to other oscillation problems of number theoretical interest.     

某些一致分布的点集序列

本文借助于“倒根函数”和矩阵构造定义了［０,１）Ｓ（Ｓ≥１）中的一些有限点集,给出了它们的偏差的上界估计,从而证明了由它们组成的点集序列是一致分布的．     

The Doubly-Pareto Uniform Distribution with Applications in Uncertainty Analysis and Econometrics

In this paper we present a novel four parameter continuous univariate distribution that can be motivated from at least two approaches. The first one views the distribution as a generalization of the uniform one that allows for uncertainty specification at the vicinity of its bounds (gradually) represented via two Pareto tails. The second one is that of an asymmetric heavy-tailed, peaked distribution with an unbounded domain with the property that the location of the mode is not uniquely determined but rather is described by a uniform range. Properties of the distribution are described and a maximum likelihood estimation (MLE) procedure for the mode location and the Pareto tails parameters is presented. The procedure is illustrated by means of an i.i.d. sample of standardized log-differences of quarterly monthly US certificate deposit interest rates for the period 1964–2004. The sample is constructed utilizing the Auto-Regressive Conditional Heteroscedastic (ARCH) time series model devised by the Nobel Laureate R.F. Engle (1982).     

Randomly generated polytopes for testing mathematical programming algorithms

Randomly generated polytopes are used frequently to test and compare algorithms for a variety of mathematical programming problems. These polytopes are constructed by generating linear inequality constraints with coefficients drawn independently from a distribution such as the uniform or the normal. It is noted that this class of ‘random’ polytopes has a special property: the angles between the hyperplanes, though dependent on the specific distribution used, tend to be equal when the dimension of the space increases. Obviously this structure of ‘random’ polytopes may bias test results.