关于线性算子的概率范数与算子空间

由于满足(PN-5)条件的PN空间(E,F)就是MangerPN空间(E,F,min),因此,肖建中等给出的关于PN空间上线性算子概率范数的结果有较大的局限性.本文中,在较一般的MengerPN空间上研究有关线性算子的概率范数和算子空间的问题,改进和推广了肖建中等的结果.     

统计与概率的交汇综合

将抽样、频率分布直方图和茎叶图等统计知识与概率交汇综合命题,是考试热点,下面作一个归纳,供复习参考．     

英语标准化考试评价中IRT与CTT的比较研究

考试质量的评价对教学管理决策至关重要.随着大规模标准化考试的不断涌现,对公正考试和科学评判的要求越来越高,阐述了IRT理论的原理及估算方法,并通过实证研究将IRT与经典测试理论(CTT)进行了理论比较,并基于中科院研究生院英语标准化考试的数据,从试题评价参数估计和考生能力估计等方面进行了实证对比.结果表明:IRT对项目参数的估计不依赖样本变化而变化,比CTT具有明显的稳定性;同时,IRT记分充分考虑了各个项目的性能差异,被试的得分更少雷同,更为精确.     

新旧课程标准初中“统计与概率”学习领域的比较分析

基于新旧两版数学课程标准,从目标、内容、实施及评价四个方面对初中学段“统计与概率”学习领域进行比较分析,“新版课标”凸显素养导向的课程目标,体现结构化特征的课程内容,强化问题情境的教学创设,关注多元多样的学业质量评价.根据课程标准的变化提出四条教学建议:着眼于核心素养,具体细化教学目标;着力于单元教学,整体设计教学内容;着手于信息赋能,深度融合课堂教学;聚焦于学业质量,有效开展教学评价.     

关于N.A.Menger PN-空间中概率收缩偶与非线性方程组的解的注记

引进了(Φ,Δ)-型概率收缩偶的概念,它简化并减弱了张石生给出的概率收缩偶的定义。在N.A.Menger PN-空间中研究了具有这类概率收缩偶的非线性算子方程组的解的存在性与唯一性问题。改进并推广了M.Altman,A.C.Lee,W.J.Padgett,张石生等人的相应结果。     

The lack-of-preference law and the corresponding distributions in frequency probability theory

We obtain two new distributions in frequency probability theory and demonstrate them, in particular, in the example of frequency dictionaries. One of these distributions gives a logarithmic correction to the Zipf-Mandelbrot law, and the other describes the “tails” of the distribution.     

Mixed poisson processes and the probability of ruin

In the Poisson case there is a well known formula that relates the probability of ruin to the distribution function of aggregate claims. It is shown how this formula can be generalized to the mixed Poisson case.     

Characteristics of queueing systems observed at events and the connection between stochastic intensity and palm probability

This article explores the link between the concepts of stochastic intensity and Palm probability and gives a new proof and useful extensions to the so-called PASTA property of queueing theory.     

Inequality in population weights,majority threshold and the inversion probability in the case of three states

Two-tier voting systems are prone to majority inversions, when the outcome of an election is not backed by a majority of popular vote. We study the inversion probability in a model with two candidates, three states and uniformly distributed fractions of supporters for each candidate. We show that the inversion probability in a two-tier voting system with three states eventually decreases with a majority threshold in the states and increases with the inequality in the size distribution of the states.     

Ruin probability in the presence of interest earnings and tax payments

In this paper we investigate the ruin probability in a general risk model driven by a compound Poisson process. We derive a formula for the ruin probability from which the Albrecher–Hipp tax identity follows as a corollary. Then we study, as an important special case, the classical risk model with a constant force of interest and loss-carried-forward tax payments. For this case we derive an exact formula for the ruin probability when the claims are exponential and an explicit asymptotic formula when the claims are subexponential.     

The Ruin Probability in the Presence of Extended Regular Variation and Optimal Investment

Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distribution of extended regular variation, starting from an integro-differential equation for the maximal survival probability, we find that the corresponding ruin probability as a function of the initial surplus is also extended regular variation.     

Ruin probability of the renewal model with risky investment and large claims

The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper. For claim sizes with common distribution of extended regular variation, we study the asymptotic behaviour of the ruin probability. As a corollary, we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims. This work was supported by National Natural Science Foundation of China (Grant Nos. 10571167, 70501028), the Beijing Sustentation Fund for Elitist (Grant No. 20071D1600800421), the National Social Science Foundation of China (Grant No. 05&ZD008) and the Research Grant of Renmin University of China (Grant No. 08XNA001)     

On the conditional probability density functions of multivariate uniform random vectors and multivariate normal random vectors

It is shown that the conditional probability density function of Y₁ given (1/n) Σ_i=1ⁿ Y_i=1Y_i^t = Σ, where Y₁, Y₂,…, Y_n are i.i.d, p-variate uniform random vectors with mean 0 equals to that of Y₁ given (1/n) Σ_i=1ⁿ Y_iY_i^t,…, Y_n are i.i.d, p-variate normal random vectors with mean 0 and covariance matrix Σ.     

Relation between the rate of convergence of strong law of large numbers and the rate of concentration of Bayesian prior in game-theoretic probability

We study the behavior of the capital process of a continuous Bayesian mixture of fixed proportion betting strategies in the one-sided unbounded forecasting game in game-theoretic probability. We establish the relation between the rate of convergence of the strong law of large numbers in the self-normalized form and the rate of divergence to infinity of the prior density around the origin. In particular we present prior densities ensuring the validity of Erd?s–Feller–Kolmogorov–Petrowsky law of the iterated logarithm.     

The finite-time ruin probability in the presence of Sarmanov dependent financial and insurance risks

Consider a discrete-time insurance risk modelWithin period i, i ≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively.Assume that {(Xi, Yi), i ≥ 1} form a sequence of independent and identically distributed random vectors following a common bivariate Sarmanov distributionIn the presence of heavy-tailed net insurance losses, an asymptotic formula is derived for the finite-time ruin probability.