独立性检验

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。

The text introduces the probability of random events and issues of counter-examples; discrete random variables related to the distribution and continuous random variable distribution of counter-examples; independence and related issues in the Phase capacitive on the counter-examples; number of characteristics of the random variable The counter-examples of; parameters estimates and assumptions in the anti-testing case of problems.

该文主要介绍了随机事件及其概率问题中的反例；有关离散型随机变量分布和连续型随机变量分布中的反例问题；独立性与相关性相容性问题中的反例介绍；有关随机变量数字特征的反例探讨；有关参数估计与假设检验中的反例问题。

Secondly, by the P-L estimation of survivor function, this paper proposed the regression models of polynomial cumulative hazard function distribution models, respectively in the case of complete date and random right censoring date; meanwhile generalized least squares estimations of unknown parameters were proposed respectively using two steps algorithm and principal component analysis algorithm.

与已有的关于多项式危险函数模型的研究成果相比，首先本文在统计模型的构造上充分考虑了累积危险函数乘积限估计量的非独立性，给出了协方差矩阵的估计；其次在模型检验方面，本文利用非参数回归分析方法，充分利用了数据本身的信息，减少了对回归关系假定的主观因素，因而分析结果更为可靠。

However, in some situations, models are hard to satisfy these assumptions at the same time. We meet a number of random errors with serial correlation and heteroscedasticity in practical problems. The rationality of these assumptions for random errors is doubtable. Therefore, it is necessary to test for correlation and heteroscedasticity in regression, which is an important step of dealing with regression problems and plays an important role in theory and practice.

但实际问题中，回归模型很难同时满足Gauss-Markov的三个假设，人们在实际问题中发现许多随机误差出现序列相关和方差不同的现象，因此对回归模型的随机误差的独立性和方差齐性的假设产生了质疑，从而展开了回归模型的相关性和异方差检验的研究，它是处理回归问题的重要步骤，在理论和应用上都有十分重要的意义。

RESULTS: The author tested the generator with 500 random numbers in NIST FIPS 140 1 and χ2 R Squared test and the result showed that it fitted the need of independent and uniform distribution.

结果：生成的500个随机数通过了NIST FIPS 140 1和χ2拟合优度检验（α=0.05），表明本方法所生成的随机数满足独立性和分布均匀性的要求。

The author discussed the vice of pseudo random number generators just mentioned above and reviewed the tests of random numbers, such as parameter test, uniform test, independent test, etc. The article also introduced the industrial test programs: Diehard, Crypt-X, ENT, NIST FIPS 140-1 and SASD.

本研究讨论了算法随机数生成器的缺陷，回顾了目前随机数的检验方法，如参数检验、均匀性检验、独立性检验和组合规律检验等，简要介绍了常用的工业检验方法—Diehard、Crypt-X、ENT、NIST FIPS 140-1和SASD。

In statistical analysis of ordinal data, we usually build up linear-by-linear association model and meet a trouble of choice of scores. Graubards et a1 (1987) proposed several methods for score choice in independence test in ordinal 2×κ contingency tables: equally spaced scores, midpoint scores and midrank scores. He also pointed out that the result of independence test may be different for the different choice of scores according to the same association model. Agresti et a1 (1987) treated the score vector in row effects and column effects model for two-way contingency tables as parameters and derived the necessary and sufficient condition of the solution under monotone order restriction by Kuhn- Tucker conditions.

在有序数据的统计分析中，通常要建立线线相关模型，其中得分的选取是一个棘手的问题，Graubard et a1（1987）给出了有序2×κ列联表中独立性检验的几种得分选取方法：等距离得分，中点得分和midrank得分等，同时指出，对于同一个相关模型，独立性的检验会由于得分选取的不同而得到不同的结论，Agresti et al（1987）把二维列联表中的行效应和列效应模型中的得分向量作为参数，在满足递增的序关系情况下，利用Kuhn-Tucker条件给出了解的充要条件。

Then we used x〓 test to test independence of each other and coincidence of syndromes.

随机抽取近10年血管性痴呆的住院病例，采用常规辨证和脑血辨证两种方法进行辨证，应用统计学方法进行独立性检验，检验两种诊断结果的一致性，并计算证候符合率。

Wavelet Deubechies lower-estimated the effect of clutter as well as the residual of the Gaussian noise and the independence of test results demo.

详细说明： Deubechies小波核下的杂波估计效果以及残留噪声的高斯性和独立性检验实验结果演示程序。

The independence test of temperature and precipitation with X2 of the El Nino event reveals that there is no significant effect of the El Nino and La Nina events on the annual temperature and annual precipitation in the drainage basin.

流域气温、降水与厄尔尼诺的X2独立性检验表明，EL Nino与LaNina事件对流域年均气温和年降水不存在显著的影响。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。