分布参数

Events,Operation and Relation of Sets, Classical Probability, Geometrical Probability , Statistical Stability of a Frequency, Axioms of Probability, Conditional Probability, Total Probability Theorem, Bayes' Rule,Independent Events,Independent Repeated Trials, One Dimensional Random Variables, Discrete Random Variables, Distribution Function of a Random Variables , Continuous Random Variables, Normal Distribution, Distribution of a Function of a Random Variable, Multidimensional Random Variables, Joint Distribution Function, Marginal Distribution Function,Discrete Two—Dimensional Random Variables,Continuous Two—Dimensional Random Variables, Independent Random Variables, Distribution of Functions of Random Variables,Expectation,Variance, Covariance, Coefficient of Correlation, Bivariate Normal Distribution, Law of Large Numbers, The Central Limit Theorems, Sample and Population ,Chi—Squared, T and F Distributions , Sampling Distributions , Point Estimation , Interval Estimation , Testing Hypotheses , A Test of Significance for Parameters in a Single Sample From a Normally Distributed Population , A Test of Significance for Parameters in Two Sample From Normally Distributed Populations .

本课程的主要内容：概率的概念与运算、随机变量及其分布、随机变量的数字特征与极限定理、数理统计的基本概念、估计和检验的基本方法，随机事件与概率随机事件、事件的关系与运算、几何概率、统计概率等，条件概率、全概率公式、贝叶斯公式、事件的独立性、二项概率公式，随机变量的概念、离散型随机变量、随机变量的分布函数、连续型随机变量、随机变量函数的分布，多维随机变量及其分布函数、边缘分布函数、随机变量的独立性、二维随机变量函数的分布，数学期望、方差、协方差和相关系数、大数定律、中心极限定理，总体与样本， X 2-分布、 t-分布和 F-分布，统计量及抽样分布，假设检验的基本概念、单个正态总体参数的显著性检验、两个正态总体参数的显著性检验。

This approach not only inherits the advantages of absolute density based algorithms which can discover arbitrary shape clusters and are insensitive to noises , but also efficiently solves the following common problems: clustering results are very sensitive to the user-deflned parameters, reasonable parameters are hard to be determined, and high density clusters are contained fully in coterminous low density clusters. With this approach, incremental clustering can also be supported effectively by defining the affected sets and seed sets of the updating objects in this approach.

聚类算法的有效性问题主要表现在三个方面：其一，聚类算法大多要求用户输入一定的参数，例如希望产生的簇的数目，而这些参数通常难以确定，特别是针对高维空间中稀疏分布的实际应用数据集，用户几乎无法给出合适的算法参数，因此非专业用户需要与数据分析专家密切配合才能保证获得理想的聚类结果，导致算法的使用极为不便；其二，聚类结果对于输入的参数值过于敏感J，往往参数值的一些轻微变化却产生聚类结果的很大差异；其三，对于高维的实际应用数据集，其数据分布往往是稀疏的、杂乱的，很难为算法选择全局的参数进行准确的聚类分析，使得聚类的质量难以保证。

The main research work of this paper are focused on following areas:(1) Based on review of the theory and methods on measurements of particle fields, a new idea for obtaining particle size and velocity distribution within a spray through imaging the particle field with a laser light sheet was put forward;(2) A DPIV (Digital Particle Image Velocimetry) system, is fit for velocity measurements of low speed flows, was developed and expended to particle size distribution measurement;(3) An arithmetic for particle velocity field reconstruction was developed, and the velocity distribution of water mist was also obtained;(4) A software system for particle analysis, which based on image geometry emend, de-noise and image partition was developed, the parameters such as particle size distribution, mean diameter, number of particles, minimum and maximum diameter can be got with this system;(5) A water mist system was developed and its characteristics, such as droplet velocity, size distribution, number of droplets and spray cone angle under different conditions were obtained from experiments with PIVS;(6) The measurement results of water mist characteristics with PIVS were compared and analyzed with the simply simulated results, and in addition, in order to verify the accuracy of PIVS, some experiments were conducted with the standard particles, such as glass-ball with known mean diameter of 50μm and 115μm, metallic coated tracing particle with mean diameter of 12μm;(7) Some experimental studies on interaction of water mist with liquid pool fires were conducted.

本论文的主要工作包括以下几个方面：（1）在对粒子场测量的相关理论和具体方法进行综述分析的基础上，提出了通过采用激光片光对粒子场进行成像以获取其粒径和速度等参数分布的新思路；（2）研制了适宜于低速流动速度场测量的DPIV(Digital Particle Image Velocimetry)系统，并使其实现了对粒子场粒径分布的测量功能；（3）研制了基于粒子运动轨迹的速度场重建算法，获取了细水雾雾场的速度分布；（4）研制了基于几何校正、去噪、图象分割等图象处理方法的"粒度分析软件系统"，该系统既可分析给出粒子场的粒径分布直方图和平均粒径，还可给出粒子的数目以及最大、最小粒径等信息；（5）建立了一细水雾发生系统，并应用上述方法对不同压力条件下细水雾系统的雾场特性（如速度分布、雾滴粒径分布、雾滴的数目、喷雾张角以及雾化长度等）进行了实验测量研究；（6）对细水雾特性参数的PIVS测量结果与计算机简单模拟计算结果进行了定性比较分析，并利用平均粒径为50μm和115μm的玻璃球以及12μm的标准示踪粒子对PIVS系统的粒径和速度测量结果进行了实验验证，同时对其局限性进行了分析讨论；（7）对不同工况条件下细水雾与油池火相互作用的过程进行了模拟实验研究。

The nonlinearity and discrete gradient inherited in CAViaR model is a conundrum for parameter estimation. We take the asymmetric Laplace distribution with scale parameter as the error process; indicate the variance has a minimum positive value when the scale parameter is a constant, conflicting with the distribution of real financial data. Further we estimate the parameters of indirect TARCH-CAViaR model base on Bayesian framework and Markov chain Monte Carlo method. The optimal scale parameter can also be obtained by Markov chain Monte Carlo method.

CAViaR一般模型中递归分位回归方程的非线性和非连续可微性是参数估计的一个难题，基于含有尺度参数的不对称拉普拉斯分布作为误差过程，指出将尺度参数固定为常数会导致不对称拉普拉斯分布随机变量的方差存在最小正值的限制，与实际金融数据分布不符；进而提出采用贝叶斯分析和马尔科夫链蒙特卡罗模拟方法，估计间接TARCH-CAViaR模型的参数，并可获得尺度参数的合理估计。

Because of its easily calculating and its accurately description parametric method has became mainstream in study field, polynomial hazard function distribution model was a large class of parametric models, when the dates are not readily handled by one of the common models such as exponential distribution or Weibull distribution, polynomial hazard function model always be used to provide adequate fits of the dates.

随着该学科的发展，大量参数、非参数方法相继提出，特别是生存分析的参数方法，以其处理简便、描述准确成为生存分析研究的主流方向。多项式危险函数模型是参数模型中的一大类，当一批数据不能用熟知的一些分布，诸如Weibull分布、对数正态分布进行很好的描述时，常常使用多项式危险函数模型。

Based on it, the research content of this dissertation has been determined. Tuan Shan River Bridge is selected as an example and APDL is used to analyze the elastic properties. After calculating the internal force influence surface of assembly skew hollow slab bridge, the internal force-controlling section is attained; the transverse distribution of internal force is studied and the transverse distribution coefficient is parametric analyzed. Based on the results, relation formula of transverse distribution coefficient between skew and perpendicular bridges are fitted. Practical calculation method for the internal force calculation of assembly skew hollow slab bridge is offered. Some conclusions are drawn from comparing and analysing the internal force, bearing reaction and deformation of both assembly and monolithic skew slab bridges.

本文对装配式斜交空心板桥的发展现状进行了综述，从此出发，确定了本文的研究内容，以团山河大桥为工程背景，采用ANSYS 提供的参数化语言APDL，对装配式斜交空心板桥弹性特性进行全面分析，计算了装配式斜交空心板桥的内力影响面，得到内力控制截面；同时计算了内力的横向分布影响线和横向分布系数，并对内力横向分布系数进行了参数分析；基于参数分析的结果，拟合了装配式斜交空心板桥与对应正交桥内力横向分布系数的关系式，为装配式斜交空心板桥的内力计算提供了实用计算方法；对比分析了装配式斜板桥与整体式斜板桥的内力、支座反力以及变形特点，得出了一些有益结论。

At each level, the parameters, hyper parameters and model parameters are adjusted to minimize the Kullback-Leibler divergence between their posteriors and real distributions so that the variable free energy can approach the real free energy.

在指出证据框架和自由能最小化方法等贝叶斯推理方法的局限性的前提下，通过对比证据框架的方法，提出了自由能框架的概念，将通常难以求解的自由能最小化过程分解成参数自由能最小化、超参数自由能最小化、模型参数自由能最小化等层次，在每个层次上调节参数、超参数和模型参数，使其后验分布为其真实分布之同的Kullback-Leibler距最小，以使可变自由能逼近真实自由能。

In view of the peaked and fat-tailed characteristics of financial return data distribution and its effect of clustering fluctuation and especially the "leverage effect" of fluctuation on VaR estimates and some efficiencies when estimating VaR with various assumptions of return data distribution,a semi-parameter approach based on EGARCH-VaR model is developed.

在综合考虑了金融收益数据分布的尖峰厚尾特征及其波动集群性，尤其是其波动的&杠杆效应&对VaR估计的影响以及各种假定收益率分布在计算风险价值时存在不足的基础上，提出了基于EGARCH-VaR的半参数方法，并且与正态分布和t分布假设下的GARCH模型的VaR计量方法进行比较，通过实证分析，并利用后验测试，表明基于EGARCH-VaR的半参数方法对风险价值的测度优于正态分布和t分布假设下GARCH模型的VaR计量方法。

According to the practical characteristics and parameters during hot finishing rolling process of aluminium alloy JP1235, a three-dimensional thermo-mechanical coupled elastic-plastic FEM model was established with the software Marc. And this model was used to simulate the rolling state of F1 stand without back tension. The lateral distribution of rolling force、contact friction force and other mechanic parameters were calculated. Meanwhile, simulated the rolling state considering the influence of mill tilt, and studied the distribution of the mechanics under this state, discussed the effect of mill tile on mechanic parameters and strip steering, which can provide some reference to steering control strategy.

根据JP1235铝合金板带热精轧过程的实际工艺特点和工艺参数，采用非线性有限元软件Marc，建立一个三维热力耦合弹塑性有限元模型，模拟了精轧机组第一机架（F1机架）失去后张力作用后的轧制状态，计算出轧制过程中轧制力、摩擦力等力能参数沿板宽方向上的分布情况，在此基础上，模拟初始轧辊倾斜影响下的轧制状态，并对该轧制状态下的力能参数分布情况进行研究，探讨轧辊倾斜对力能参数分布及跑偏规律的影响，为纠偏控制提供了一定的理论依据。

First,owing to the wide range of use of WeibuU distribution,we propose the Weibull MTD model,which has improved the MTD model based on Gaussian distribution in some thick-tailed cases;Second,some stationarity properties of the model are discussed;After that,we apply the standard EM algorithm to mixture models to get the estimation equations and then expose bootstrap method to calculate confidence region of the parameters;Finally,some simulations and an example are analyzed in detail,which show that when analyzing nonstandard date,such as financial date,insurance date and so on,it is more proper for estimation to use the Weibull MTD model than the Gaussian MTD model.

首先给出基于Weibull分布的混合转移分布模型的一阶与k阶平稳的充分必要条件；接着，应用EM算法，得到了参数的极大似然估计及它们的标准误差；然后，应用Bootstrap方法，得到了参数的置信区间；最后，通过模拟与实例分析，说明该模型在分析来自金融、保险等某些厚尾分布的数据时，在参数估计方面的表现优于高斯混合转移分布模型。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。