Exact Distribution of Difference of Two Sample Proportions and Its Inferences

Comparing two population proportions using confidence interval could be misleading in many cases, such as the sample size being small and the test being based on normal approximation. In this case, the only one option that we have is to collect a large sample. Unfortunately, the large sample might not be possible. One example is a person suffering from a rare disease. The main purpose of this journal is to derive a closed formula for the exact distribution of the difference between two independent sample proportions, and use it to perform related inferences such as a confidence interval, regardless of the sample sizes and compare with the existing Wald, Agresti-Caffo and Score. In this journal, we have derived a closed formula for the exact distribution of the difference between two independent sample proportions. This distribution doesn’t need any requirements, and can be used to perform inferences such as: a hypothesis test for two population proportions, regardless of the nature of the distribution and the sample sizes. We claim that exact distribution has the least confidence width among Wald, Agresti-Caffo and Score, so it is suitable for inferences of the difference between the population proportion regardless of sample size.

L-Moments and TL-Moments as an Alternative Tool of Statistical Data Analysis

Moments and cumulants are commonly used to characterize the probability distribution or observed data set. The use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. The moment method does not always produce satisfactory results. It is difficult to determine exactly what information concerning the shape of the distribution is expressed by its moments of the third and higher order. In the case of small samples in particular, numerical values of sample moments can be very different from the corresponding values of theoretical moments of the relevant probability distribution from which the random sample comes. Parameter estimations of the probability distribution made by the moment method are often considerably less accurate than those obtained using other methods, particularly in the case of small samples. The present paper deals with an alternative approach to the construction of an appropriate parametric distribution for the considered data set using order statistics.

基于正态变换的变样本容量Shewhart比例控制图设计

为了提高Shewhart型比例控制图的监控效率,将其与变样本容量策略结合,提出一种新的比例控制图(VSS Shewhart-RZ*控制图)来监控二元正态变量之比。基于正态变换方法设计了新的比例统计量Z*,以消除样本容量变化对比例控制图设计及使用的不利影响。采用马尔科夫链方法计算了该控制图的平均运行长度和平均样本容量,给出该控制图的参数优化算法。通过仿真分析研究了该控制图的统计性能,并与Shewhart比例控制图进行比较,结果表明VSS Shewhart-RZ*控制图的性能明显优于传统固定样本容量Shewhart比例控制图。

基于哈希桶和聚类的变半径邻域粗糙集模型

邻域粗糙集是处理机器学习与数据挖掘中不确定性的数据分析工具.邻域粗糙集中邻域粒的大小往往受邻域半径的影响.针对现有的邻域粗糙集模型通常对每个样本设置相同的邻域半径,导致得到的邻域粒无法对每个样本进行准确地刻画的问题,基于样本数据的分布信息,首先对数据集进行聚类,并基于哈希桶对每个类的样本分布情况做出分析,然后为每个样本设置合适大小的邻域半径,使其能够更准确地刻画每个样本的信息,进而提出变半径邻域粗糙集模型.最后选取了8个UCI数据集进行实验,并分别与当前最常用的邻域粗糙集模型进行比较,理论分析与实验结果表明所提出的变半径邻域粗糙集模型具有更好的学习性能.

Pressure distribution feature-oriented sampling for statistical analysis of supercritical airfoil aerodynamics

In the field of supercritical wing design, various principles and rules have been summarized through theoretical and experimental analyses. Compared with black-box relationships between geometry parameters and performances, quantitative physical laws about pressure distributions and performances are clearer and more beneficial to designers. With the advancement of computational fluid dynamics and computational intelligence, discovering new rules through statistical analysis on computers has become increasingly attractive and affordable. This paper proposes a novel sampling method for the statistical study on pressure distribution features and performances, so that new physical laws can be revealed. It utilizes an adaptive sampling algorithm, of which the criteria are developed based on Kullback–Leibler divergence and Euclidean distance.In this paper, the proposed method is employed to generate airfoil samples to study the relationships between the supercritical pressure distribution features and the drag divergence Mach number as well as the drag creep characteristic. Compared with conventional sampling methods, the proposed method can efficiently distribute samples in the pressure distribution feature space rather than directly sampling airfoil geometry parameters. The corresponding geometry parameters are searched and found under constraints, so that supercritical airfoil samples that are well distributed in the pressure distribution space are obtained. These samples allow statistical studies to obtain more reliable and universal aerodynamic rules that can be applied to supercritical airfoil designs.

Crowdsourced Sampling of a Composite Random Variable: Analysis, Simulation, and Experimental Test

A composite random variable is a product (or sum of products) of statistically distributed quantities. Such a variable can represent the solution to a multi-factor quantitative problem submitted to a large, diverse, independent, anonymous group of non-expert respondents (the “crowd”). The objective of this research is to examine the statistical distribution of solutions from a large crowd to a quantitative problem involving image analysis and object counting. Theoretical analysis by the author, covering a range of conditions and types of factor variables, predicts that composite random variables are distributed log-normally to an excellent approximation. If the factors in a problem are themselves distributed log-normally, then their product is rigorously log-normal. A crowdsourcing experiment devised by the author and implemented with the assistance of a BBC (British Broadcasting Corporation) television show, yielded a sample of approximately 2000 responses consistent with a log-normal distribution. The sample mean was within ~12% of the true count. However, a Monte Carlo simulation (MCS) of the experiment, employing either normal or log-normal random variables as factors to model the processes by which a crowd of 1 million might arrive at their estimates, resulted in a visually perfect log-normal distribution with a mean response within ~5% of the true count. The results of this research suggest that a well-modeled MCS, by simulating a sample of responses from a large, rational, and incentivized crowd, can provide a more accurate solution to a quantitative problem than might be attainable by direct sampling of a smaller crowd or an uninformed crowd, irrespective of size, that guesses randomly.

OPTIMAL ALLOCATION FOR ESTIMATING THE CORRELATION COEFFICIENT OF MORGENSTERN TYPE BIVARIATE EXPONENTIAL DISTRIBUTION BY RANKED SET SAMPLING WITH CONCOMITANT VARIABLE

Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variable X which is correlated with the study variable Y, where （X, Y） follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficient p of the random variables X and Y when the auxiliary variable X is used for ranking the sample units and the study variable Y is measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators of p when the mean 0 of the study variable Y is known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator of p under the optimal allocation in the case of known θ is reformed for estimating p in the case of unknown θ, and the reformed estimator is shown to be strongly consistent.

Extended Rama Distribution:Properties and Applications

In this paper,the Rama distribution(RD)is considered,and a new model called extended Rama distribution(ERD)is suggested.The new model involves the sum of two independent Rama distributed random variables.The probability density function(pdf)and cumulative distribution function(cdf)are obtained and analyzed.It is found that the new model is skewed to the right.Several mathematical and statistical properties are derived and proved.The properties studied include moments,coefficient of variation,coefficient of skewness,coefficient of kurtosis and moment generating function.Some simulations are undertaken to illustrate the behavior of these properties.In addition,the reliability analysis of the distribution is investigated through the hazard rate function,reversed hazard rate function and odds function.The parameter of the distribution is estimated based on the maximum likelihood method.The distributions of order statistics for ERD are also presented.The performance of the suggested model is compared with several other lifetime distributions based on some goodness of fit tests on a real dataset.It turns out that the suggested model is more flexible than its competitors considered in this study,for modeling real lifetime data.

基于改进联合分布适应的轴承智能故障诊断方法

在轴承故障诊断过程中,存在缺乏足量故障样本、变工况下信号分布差异等问题。虽然基于机器学习和深度学习方法的智能故障诊断方法的运用取得了许多成果,但该方法在应用过程中仍面临一些挑战,阻碍了智能故障诊断方法在实际工业场景下的应用。为此,提出了一种基于改进联合分布适应的轴承智能故障诊断方法(BIFD-IJDA)。首先,利用小波包变换对振动信号进行了分解与重构,再计算了重构信号的统计参数,构成了原始特征集;然后,设计了基于特征重要度与KL散度的迁移特征选取方法,对各统计参数特征进行了量化评估;采用了改进联合分布适应方法,对源域和目标域特征集进行了分布适应处理,降低了域间分布差异;最后,利用源域特征样本训练的故障诊断模型预测了目标域样本故障类别,采用美国凯斯西储大学实验台和机械故障模拟(MFS)实验台的轴承故障数据,开展了不同工况下的故障诊断实验。实验结果表明:该故障诊断方法在2种轴承故障数据下取得的最大故障诊断准确率分别为100%和96.29%,明显优于其他对比模型。研究结果表明:该故障诊断方法具有应用于实际工业场景的潜力。

SNARC效应量大小及置信区间的可信问题的实例分析

通过实例分析SNARC效应量和置信区间可信度问题。(1)效应量是心理学实验结果报告中一个非常重要的部分,依据SNARC效应量的特殊性提出一种新的统计方法(在线性回归模型中引入混合虚拟变量)处理Aleottia等(2020)的开放实验数据,尽管该方法比一般方法更复杂。(2)参数的区间估计是一种基本统计推断形式。根据枢轴量分布,置信区间在一定置信度下可估计总体参数所在的可能范围。文章通过构建一个特殊实例分析了置信区间的估计过程,并和假设检验、贝叶斯统计进行对比分析,结果显示,虽然置信区间可以用来估计参数,但是存在依据某置信区间无法作出正确估计的情况,通过贝叶斯统计能分析出其中原因。

基于统计抽样原理的典型室温分布比例确定方法研究

基于统计抽样原理,以河南濮阳某小区的室温采集系统为研究对象,选择不同的抽样方法,通过比例区间估计推断了小区室温分布,并比较了不同抽样比例下的推断结果。结果表明,分层随机抽样方式与分层系统抽样、整群抽样相比有明显优势,当室温抽样比例大于8%时,可满足各分项统计指标的要求。研究结果可为典型室温比例的确定提供参考和依据。

国家产品质量监测制度:调查方案与实践应用

国家产品质量监测制度在我国政府质量评价中,发挥着越来越广泛的作用。样本量确定、样本量分配、实际精度计算、结果应用等,是该制度的重要内容。常规的统计调查设计,一般基于精度要求等计算样本量,而国家产品质量监测制度采用复杂的多阶段抽样。除精度要求外,还要结合各阶段现实条件的限制,综合使用辅助信息,探讨如何确定初始样本量、开展样本量分配。本文针对国家产品质量监测样本量设定与分配等关键问题,对我国现行模式加以梳理,对监测得出的统计数据进行分析,为产品质量监测制度的完善对策提供参考。研究发现:(1)我国各省(区、市)产品质量水平“南北方地区差异”进一步凸显;(2)学生、儿童、老人、残疾人等特殊群体专用产品质量仍然较低;(3)城乡结合部、农村市场等领域低质低价产品需求旺盛;(4)部分产业链上下游质量整体水平不高。

对流层大气温度统计模型研究

为了获得地理位置上随高度变化的大气温度统计特性,基于有限的对流层大气温度观测数据,根据谐波规律给出了大气温度的统计均值和方差,并采用观测数据的相关性矩阵和随机变量,建立了对流层大气温度统计模型。根据模型和方法,统计分析后可以得到对流层大气温度特性,经过与观测数据统计参数比较,验证了模型和方法的有效性。

建筑结构计量抽样检测推定区间的理解与计算

建筑结构检测规定了材料强度等计量抽样检测的结果,且提供推定区间。为了更好地解释推定区间的含义,不同置信度的均值和95%保证率特征值推定区间的上限值和下限值系数,利用数理统计的概念推导了推定区间系数函数所服从的概率分布,MATLAB计算程序对不同样本容量、置信度、分位数的上限值系数和下限值系数进行了计算。计算结果与规范表中的系数高度吻合,进一步验证了理论推导及计算程序的正确性,提出上限值系数和下限值系数具体的求解方法。

Application of Transfer Learningin Mechanical Equipment Intelligent Diagnosis:Literature Review

Accelerating the process of intelligent manufacturing and the demand for new industrial productivity,the operating conditions of machinery and equipment have become ever more severe.As an important link to ensure the stable operation of the production process,the condition monitoring and fault diagnosis of equipment have become equally important.The fault diagnosis of equipment in actual production is often challenged by variable working conditions,large differences in data distribution,and lack of labeled samples,etc.Traditional fault diagnosis methods are often difficult to achieve ideal results in these complex environments.Transfer learning(TL)as an emerging technology can effectively utilize existing knowledge and data to improve the diagnostic performance.Firstly,this paper analyzes the trend of mechanical equipment fault diagnosis and explains the basic concept of TL.Then TL based on parameters,TL based on features,TL based on instances and domain adaptive(DA)methods are summarized and analyzed in terms of existing TL methods.Finally,the problems faced in the current TL research are summarized and the future development trend is pointed out.This review aims to help researchers in related fields understand the latest progress of TL and promote the application and development of TL in mechanical equipment diagnosis.

土壤养分变异与合理取样数量

利用地统计学方法、地理信息系统技术 ,结合土壤养分状况系统研究法对一定条件下的土壤合理取样数量作了细致的研究。结果表明 ,大部分土壤养分都具有较为良好的半方差结构 ,空间自相关距都比较大。在平衡取样成本和精确度的前提下必须考虑土壤养分的空间变异程度。利用地理信息系统等手段可以充分表现土壤养分变异的分布情况 ,从而为设置取样点提供依据。在本研究条件下 ,利用分层取样的最适分配法获得 34 5hm2 耕地上的最佳取样数量 ,针对土壤速效钾的取样以 95 %的置信水平 1 0 %的相对误差为宜 ,取样数量为 2 4个 ;针对土壤速效磷的取样以 95 %的置信水平 2 0 %的相对误差为宜 ,取样数量 1 0个。

区域土壤重金属空间变异及合理采样数确定

为研究北京市大兴区的重金属污染情况,加强农产品安全生产管理,在北京市大兴区布设了313个取样点,测定了土壤重金属Cu、Zn、Pb、Ni、As和Hg的含量,并充分利用空间分析和地统计分析技术对土壤重金属的空间变异性及合理取样数进行了研究。结果表明:大兴区土壤中6种主要重金属空间变异系数范围为14.43%～47.16%,其变异程度为As>Zn>Cu>Ni>Hg>Pb,且这些土壤重金属均在一定范围内存在空间相关性,空间相关距排列为Cu>Zn>Pb>Hg>As>Ni。相比于经典统计法,地统计分析和克立格插值考虑了空间结构性和随机性,可以确定更合理的采样数量。

植烟土壤养分的空间变异特征及适宜性评价——以重庆市彭水县为例

采用域法对彭水县植烟土壤养分数据特异值进行处理,利用K-S检验数据的分布特征,并采用半方差、克立格插值法研究了植烟区土壤肥力的空间变异特征.从变异系数看,土壤速效磷最大为71.60%,而pH最小,仅为12.57%;土壤肥力养分样本数据最佳拟合模型为指数模型;土壤养分在空间上有一定的自相关性,并受各向异性的影响,自相关阈值变幅表现为pH>有机质>有效磷>有效氮>CEC>速效钾;土壤养分的随机变异表现为pH>有效磷>有效氮>有机质>CEC>速效钾,CEC、速效钾具有中等空间相关性,其他肥力要素为空间弱相关性;彭水县植烟土壤酸碱度、有效氮、有效磷含量比较适宜植烟,阳离子交换量、有机质含量对烤烟生产的适应性好,土壤速效钾非常适宜于植烟.因此,通过对空间分布格局图的实地分析,可以从宏观上把握影响土壤养分空间变异的因素,从而做出科学的作物的适宜性评价.

田间土壤特性的空间变异性

在田间对土壤的一些基本特性参数──体积密度、初始含水率、饱和含水率、饱和水力传导度和孔隙大小分布参数进行了测试。对各土壤特性参数实测样本的统计分析结果表明，所选定的试验田块中除孔隙大小分布参数服从对数正态分布外，其他参数均服从正态分布。根据各参数在该田块内的等直线分布图，分析了参数的空间分布特征。

黄河三角洲土壤盐分空间变异性与合理采样数研究

以黄河三角洲地区一块约520hm^2的田块为研究区，采用经典统计学和地统计学方法进行不同层次土壤盐分（0～20cm，20～60cm，60～100cm，100～140cm）的空间变异及其合理采样数量研究。结果表明：研究区土壤盐分普遍较高且表聚作用明显；各层土壤盐分均属于中等变异强度;受结构性因素和随机性因素的共同作用，各土层盐分均具有中等的空间相关性。对Kriging插值结果分析表明，土壤盐分的空间分布受微地形和气候条件的影响较大．且研究区各土层盐分分布存在着空间上的相似性。应用Cochran公式和分层采样方法对合理采样数量进行了分析，发现采用分层采样方法可以有效降低采样数量，且采用最适分配法可以获得最为理想的采样数量，该方法较比重分配法采样数降低幅度最大达35％左右。该研究为黄河三角洲地区盐渍土地的科学管理、改良以及利用提供一定的理论依据和技术参考。