泊松积分在概率论中的应用

文章介绍了泊松积分在正态分布、二维正态分布、对数正态分布等问题中常见的应用,并给出了具体的例子。     

泊松积分在波动方程中的应用

本文通过对泊松方程和波动方程有关知识的简单介绍,利用二维及三维波动方程的求解的过程,详尽地介绍并证明了泊松积分在波动方程中的应用。在介绍应用时,我们主要采用了一些比较典型的例题,理论联系实际地探讨泊松积分在波动方程中的应用。     

浅析二项分布、泊松分布和正态分布之间的关系

二项分布、泊松分布和正态分布一直是学习和研究概率统计的基础。在一定条件下,这三个分布之间存在着密切关系。文章通过求极限分布,研究了二项分布与泊松分布、二项分布与正态分布之间的关系,并利用特征函数和分布函数相互唯一确定这一性质,分析了泊松分布和正态分布之间的关系。     

浅析二项分布、泊松分布和正态分布之间的关系

二项分布、泊松分布和正态分布一直是学习和研究概率统计的基础.在一定条件下,这三个分布之间存在着密切关系.文章通过求极限分布,研究了二项分布与泊松分布、二项分布与正态分布之间的关系,并利用特征函数和分布函数相互唯一确定这一性质,分析了泊松分布和正态分布之间的关系.     

泊松过程在证券投资分析中的应用

本文视证券价格的波动为动态的泊松过程,对中国证券投资市场的证券价格的变化规律进行了分析。在此基础上,计算出泊松过程理论下的证券价格的期望值、证券投资收益率的期望值、收益率的方差。通过区间估计选择证券,对其建立证券市场的投资组合模型,从而判断证券市场中长期的总体走势方向,为证券投资者买卖决策提供新的参考依据。     

基于泊松分布的需求预测模型设计

研究的目的是运用有效的方法来提高需求预测的准确性,从而优化物料库存控制,以解决当前困扰生产企业的库存管理难题。通过分析物料的消耗规律,运用管理科学的理论与方法建立了基于泊松分布的物料需求模型,利用时间序列法对主要参数进行科学计算。研究的需求预测方法能够较好地解决库存控制中存在的计划问题,具有较强的可操作性,对提高企业库存管理水平具有很好的指导作用。     

基于泊松分布的钢厂备件优化模型

钢铁工业是流程型工业,重要配件对生产过程至关重要,因此在钢铁钢铁企业中备件管理问题就显得尤为突出。备件管理是钢铁钢铁企业设备管理工作中的一项重要内容,它直接影响设备的维护、检修、抢修工作,与钢铁企业的正常生产和经济效益密切相关。做好钢铁企业备件管理工作的核心是做好备件计划。本文基于泊松分布．考虑备件的订货成本、持有成本、缺货成本、特别订货成本,给出了最优备件库存量及最优成本。     

索赔次数为零膨胀泊松过程的风险模型

零膨胀泊松分布在应用中经常用来描述零过多的计数数据,文章根据零膨胀泊松分布定义了一类零膨胀泊松过程,并研究了零膨胀泊松过程的相关分布性质。考虑以零膨胀泊松过程作为计数过程的风险模型,给出该模型惩罚函数满足的更新方程,作为特例,当索赔额服从指数分布时给出破产概率的解析表达式。     

基于泊松分布的可修复航材库存控制模型研究

在分析可修复航材需求规律的基础上,考虑正规仓库容量大小,结合启用临时仓库条件,提出一种基于泊松分布的可修航材库存控制模型,给出了求解方法,并进行了实例计算,计算结果表面,模型符合航材保障实际,计算简单方便,便于工程应用。     

贯穿概率论的n重贝努里概型

以n重贝努里概型为基础,利用极限分布,讨论了概率论中最常见的二项分布、泊松分布、指数分布、正态分布之间的关系,从而得到n重贝努里概型贯穿概率论教程的结论。     

A new conditional specification of the bivariate Poisson conditionals distribution1

The bivariate Poisson conditionals distribution is characterized by the form of one of the conditional distributions and one of the conditional expectations.     

On a study of the exponential and Poisson characteristics of the Poisson process

Based on the exponential and Poisson characteristics of the Poisson process, in this work we present some characterizations of the Poisson process as a renewal process. More precisely, let γ_t be the residual life at time t of the renewal process A={A(t),t≥0 }, under suitable condition, we prove that if Var(γ_t)=E ² (γ_t),∀t≥0, then A is a Poisson process. Secondly, we show that if Var (A(t)) is proportional to E (A(t)), then A is a Poisson process also, and Var (A(t))=E (A(t)). Received: August 1999     

A bivariate Poisson count data model using conditional probabilities

The applied econometrics of bivariate count data predominantly focus on a bivariate Poisson density with a correlation structure that is very restrictive. The main limitation is that this bivariate distribution excludes zero and negative correlation. This paper introduces a new model which allows for a more flexible correlation structure. To this end the joint density is decomposed by means of the multiplication rule in marginal and conditional densities. Simulation experiments and an application of the model to recreational data are presented.     

Tests for zero inflation in a bivariate zero‐inflated Poisson model

The score test statistics for testing zero inflation and covariance parameter are proposed in the bivariate zero‐inflated Poisson (BZIP) regression model. The Monte Carlo studies show that the score test and likelihood ratio test for testing zero inflation underestimate the nominal significance level, while the score test for covariance parameter keeps the significance level close to the nominal one. To overcome this nominal level underestimation, we propose a bootstrap method of the score test for the testing problem of zero inflation. An empirical example with covariates is provided to illustrate the results. In addition, score test for zero inflation is also proposed in the BZIP model, which allows a flexible dependence structure using copula.     

基于泊松分布的兰州冻品市场面积估算

预测在我们的日常生活中起着非常作用,长久以来人们总结并归纳出的定性定量的预测方法很多。文章根据调查方法的特殊性用运概率中的离散和连续型概率方法分别对调查数据进行拟合,进而找到符合数据分布的分布规律并进行预测。     

Goodness-of-fit tests for Poisson count time series based on the Stein–Chen identity

To test the null hypothesis of a Poisson marginal distribution, test statistics based on the Stein–Chen identity are proposed. For a wide class of Poisson count time series, the asymptotic distribution of different types of Stein–Chen statistics is derived, also if multiple statistics are jointly applied. The performance of the tests is analyzed with simulations, as well as the question which Stein–Chen functions should be used for which alternative. Illustrative data examples are presented, and possible extensions of the novel Stein–Chen approach are discussed as well.     

Probability Integrals of the Multivariate t Distribution

Results on probability integrals of multivariate t distributions are reviewed. The results discussed include: Dunnett and Sobel's probability integrals, Gupta and Sobel's probability integrals, John's probability integrals, Amos and Bulgren's probability integrals, Steffens' non‐central probabilities, Dutt's probability integrals, Amos' probability integral, Fujikoshi's probability integrals, probabilities of cone, probabilities of convex polyhedra, probabilities of linear inequalities, maximum probability content, and Monte Carlo evaluation.