浅谈随机变量在实际中的应用

随机变量是概率论与数理统计的一个重要组成部分。本文通过对随机变量序列收敛的性质及定理的分析和研究,阐述了切比雪夫(Chebyshev)不等式和中心极限定理的理论等在实际中的应用。充分展现了随机变量序列在数学领域的重要作用,论证了切比雪夫(Chebyshev)不等式和中心极限定理在实际问题中的应用,从而得出了随机变量序列在实际问题中的解决方法,让我们对其有了更广泛和深刻的认识。     

有限维线性空间直和分解问题的新探索

线性空间直和分解问题在数学、力学及许多应用领域有着广泛的应用.本文利用哈密尔顿-凯莱定理得到了n维向量空间的一个适用范围更为广泛的直和分解定理和一些重要推论,拓展了向量空间直和分解使用范围,通过范例说明直和分解的具体方法和实际过程.     

二维连续型随机变量卷积公式探讨

本文主要讨论二维独立连续型随机变量,多数教材在求解卷积公式时采用积分变量代换,在教学中大多数学生难以明白,本文将利用微积分学基本定理对卷积公式证明,帮助学生更好的理解和掌握卷积公式,并进行实例分析。     

中心极限定理在商场管理中的若干应用

本文将随机变量的特征函数和极限理论相结合应用到商场管理中,拓宽了随机变量的特征函数和极限理论的应用领域.并给出了一个计算机随机模拟程序。     

人民币升值与股票收益率——基于单因素方差分析的实证研究

方差分析方法是1923年由英国统计学家R.A.Fisher首先提出的,其基本思想是:在相同的方差假设前提下,对方差进行变异分解,将总体方差分解到不同因素的不同水平上,考察不同因素不同水平是否对总体变异具有显著的影响,进而考察多个总体之间的均值是否有明显的不同。对观察对象而言,影响因素可以分为两大类:第一类是人为可以控制的因素,称为控制变量,第二类是人为难以控制的因素,称为随机变量,受控制变量和随机变量影响的     

关于几类混合随机变量序列定义的注记研究

本文通过对三类混合随机变量ρ混合序列,ρ*混合序列和α混合序列的定义进行联系比较,同时,例举了随机变量序列的部分和的极限性质,在概率和统计中占有十分重要的地位。     

在最终需求为服从正态分布的随机变量时的投入产出优化控制模型

本文给出了随机投入产出决策方法的特征，讨论了在最终需求为服从正态分布的随机变量时的投入产出决策方法，并且建立了相应的随机优化控制模型。     

概率统计在管理决策中的应用

一、离散型随机变量的概率分布及应用常见的离散型随机变量的概率分布有两点分布、二项分布和泊松分布。两点分布只适用于一次随机试验的简单情况,在决策管理中很少使用。二项分布是以贝努利(Bernouli)概型为背景的一     

模糊随机变量下保单现金价值计算初探

文章以三角模糊数对贴现函数模糊进行估计,利用模糊随机变量建立两全保险和生存年金模型,并通过精算现值理论得出新的现金价值计算方法,最后给出模拟算例。     

二维随机变量的分布函数

概率论与数理统计是学习现代科学技术的重要理论基础,同时它也是考研必考科目之一,在教学过程中,我遇到了这样一道题目,本文由这道概率习题联想到了几个问题:二维随机变量的分布函数是否唯一;三元三次方程组解的唯一性.     

On the Conditional Variance of Fuzzy Random Variables

The conditional variance of random variables plays an important role for well-known variance decomposition formulas. In this paper, the conditional variance is defined for fuzzy random variables and some properties are proved, which especially generalize to the mentioned variance decomposition. Moreover, results for two special types of fuzzy random variables and an outlook for possible applications are presented.     

马尔可夫性及其检验方法研究

马尔可夫链广泛应用于信息论、自动控制、通信技术、基因遗传、计算机科学、经济管理、教育管理、市场预测等领域,马尔可夫性是其最基本特征,因此,在运用马尔可夫链进行预测时,必须对预测对象以往的统计数据资料构成的随机变量序列的马尔可夫性进行检验,只有符合马尔可夫性,才能利用马尔可夫链进行预测,才能保证预测精度。本文探讨了马氏性的概念及性质,研究了马尔可夫性的检验方法,通过实例对该检验方法进行了分析。     

基于随机需求的物流配送中心选址离散模型研究

针对物流需求不确定情况下的物流配送中心选址问题,对传统模型进行改进,将随机需求变量引入离散型选址模型,利用随机规划理论和遗传算法对实例模型进行求解。结果显示物流需求不确定情况下的随机规划模型的求解结果比假设已知需求情况下的结果真实可信,所需物流费用较少。     

Asymptotic confidence intervals for the length of the shortt under random censoring

A short t of a one dimensional probability distribution is defined to be an interval which has at least probability t and minimal length. The length of a show and its obvious estimator are significant measures of scale of a distribution and the corresponding random sample, respectively. In this note a non-parametric asymptotic confidence interval for the length of the (uniqueness is assumed) short t is established in the random censorship from the right model. The estimator of the length of the short t is based on the product-limit (PL) estimator of the unknown distribution function. The proof of the result mainly follows from an appropriate combination of the Glivenko-Cantelli theorem and the functional central limit theorem for the PL estimator.     

Neyman–Pearson Lemma for Fuzzy Hypotheses Testing with Vague Data

In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which both hypotheses and observations are imprecise. This paper tries to develop a new approach for testing fuzzy hypothesis when the available data are fuzzy, too. First, some definitions are provided, such as: fuzzy sample space, fuzzy-valued random sample, and fuzzy-valued random variable. Then, the problem of fuzzy hypothesis testing with vague data is formulated. Finally, we state and prove a generalized Neyman–Pearson Lemma for such problem. The proposed approach is illustrated by some numerical examples.     

体育教学中各种练习对运动技术学习的影响

练习是体育教学中学生掌握基本运动技术与技能的基本途径,但是如何去练习,则很少有人去进行探索。为此,本文再通过对运动技能学习与控制理论的学习,结合学校体育教学实际,就其中部分常用练习方法:集中练习和分散练习;固定练习和变异练习;随机练习与段落练习以及完整练习与分解练习等进行探讨,比较各种不同的练习之间的优缺点,希望能够对体育教学提供参考。     

Stochastic DEA Models With Different Types of Input-Output Disturbances

This paper presents stochasticmodels in data envelopment analysis (DEA) for the possibilityof variations in inputs and outputs. Efficiency measure of adecision making unit (DMU) is defined via joint probabilisticcomparisons of inputs and outputs with other DMUs and can becharacterized by solving a chance constrained programming problem.By utilizing the theory of chance constrained programming, deterministicequivalents are obtained for both situations of multivariatesymmetric random disturbances and a single random factor in theproduction relationships. The linear deterministic equivalentand its dual form are obtained via the goal programming theoryunder the assumption of the single random factor. An analysisof stochastic variable returns to scale is developed using theidea of stochastic supporting hyperplanes. The relationshipsof our stochastic DEA models with some conventional DEA modelsare also discussed.     

Probability theory in fuzzy sample spaces

This paper tries to develop a neat and comprehensive probability theory for sample spaces where the events are fuzzy subsets of The investigations are focussed on the discussion how to equip those sample spaces with suitable -algebras and metrics. In the end we can point out a unified concept of random elements in the sample spaces under consideration which is linked with compatible metrics to express random errors. The result is supported by presenting a strong law of large numbers, a central limit theorem and a Glivenko-Cantelli theorem for these kinds of random elements, formulated simultaneously w.r.t. the selected metrics. As a by-product the line of reasoning, which is followed within the paper, enables us to generalize as well as to bring together already known results and concepts from literature.Acknowledgement. The author would like to thank the participants of the 23rd Linz Seminar on Fuzzy Set Theory for the intensive discussion of the paper. Especially he is indebted to Professors Diamond and Höhle whose remarks have helped to get deeper insights into the subject. Additionally, the author is grateful to one anonymous referee for careful reading and valuable proposals which have led to an improvement of the first draft.This paper was presented at the 23rd Linz Seminar on Fuzzy Set Theory, Linz, Austria, February 5–9, 2002.     

“经济人”假设下的“蛛网理论”分析

论文分析了蛛网理论中的假设与"经济人"假设之间的冲突,提出了放宽假设条件下的改进型"蛛网"模型,论述了在经济运行过程中理性变量的存在及其对经济产生的作用。     

Penalized h-likelihood approach for variable selection in AFT random-effect models

Survival models allowing for random effects (e.g., frailty models) have been widely used for analyzing clustered time-to-event data. Accelerated failure time (AFT) models with random effects are useful alternatives to frailty models. Because survival times are directly modeled, interpretation of the fixed and random effects is straightforward. Moreover, the fixed effect estimates are robust against various violations of the assumed model. In this paper, we propose a penalized h-likelihood (HL) procedure for variable selection of fixed effects in the AFT random-effect models. For the purpose of variable selection, we consider three penalty functions, namely, least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD), and HL. We demonstrate via simulation studies that the proposed variable selection procedure is robust against the misspecification of the assumed model. The proposed method is illustrated using data from a bladder cancer clinical trial.