Analysis of College Students’ Test Scores Based on Two-Component Mixed Generalized Normal Distribution

In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.

Constant-Step Stress Accelerated Life Test of VFD under Logarithmic Normal Distribution Case

In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.

Predicting stability of integrated circuit test equipment using upper side boundary values of normal distribution

In response to the growing complexity and performance of integrated circuit(IC),there is an urgent need to enhance the testing and stability of IC test equipment.A method was proposed to predict equipment stability using the upper side boundary value of normal distribution.Initially,the K-means clustering algorithm classifies and analyzes sample data.The accuracy of this boundary value is compared under two common confidence levels to select the optimal threshold.A range is then defined to categorize unqualified test data.Through experimental verification,the method achieves the purpose of measuring the stability of qualitative IC equipment through a deterministic threshold value and judging the stability of the equipment by comparing the number of unqualified data with the threshold value,which realizes the goal of long-term operation monitoring and stability analysis of IC test equipment.

ON TESTING THE EQUALITY OF K MULTIPLE AND PARTIAL CORRELATION COEFFICIENTS

Coutsourides (1980) derives an ad hoc nuisance parameter removal test for testing the equality of two multiple correlation coefficients of two independent p variate normal populations, under the assumption that a sample of size n is available from each population. He also extends his ad hoc nuisance parameter removal test to the testing of the equality of two multiple correlation matrices. This paper presents likelihood ratio tests for testing the equality of k multiple correlation coefficients, and also k partial correlation coefficients.

A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions

Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.

On Testing Equality of K Multiple Correlation Matrices

Coutsourides derived an ad hoc nuisance paratmeter removal test for testing equality of two multiple correlation matrices of two independent p variate normal populations under the assumption that a sample of size n is available from each population. This paper presents a likelihood ratio test criterion for testing equality of K multiple correlation matrices and extends the results to the testing of equality of K partial correlation matrices.

Analysis of wheel-rail adhesion redundancy considering the thirdbody medium on the rail surface

Purpose–In response to the problem of insufficient traction/braking adhesion force caused by the existence of the third-body medium on the rail surface,this study aims to analyze the utilization of wheel-rail adhesion coefficient under different medium conditions and propose relevant measures for reasonable and optimized utilization of adhesion to ensure the traction/braking performance and operation safety of trains.Design/methodology/approach–Based on the PLS-160 wheel-rail adhesion simulation test rig,the study investigates the variation patterns of maximum utilized adhesion characteristics on the rail surface under different conditions of small creepage and large slip.Through statistical analysis of multiple sets of experimental data,the statistical distribution patterns of maximum utilized adhesion on the rail surface are obtained,and a method for analyzing wheel-rail adhesion redundancy based on normal distribution is proposed.The study analyzes the utilization of traction/braking adhesion,as well as adhesion redundancy,for different medium under small creepage and large slip conditions.Based on these findings,relevant measures for the reasonable and optimized utilization of adhesion are derived.Findings–When the third-body medium exists on the rail surface,the train should adopt the low-level service braking to avoid the braking skidding by extending the braking distance.Compared with the current adhesion control strategy of small creepage,adopting appropriate strategies to control the train’s adhesion coefficient near the second peak point of the adhesion coefficient-slip ratio curve in large slip can effectively improve the traction/braking adhesion redundancy and the upper limit of adhesion utilization,thereby ensuring the traction/braking performance and operation safety of the train.Originality/value–Most existing studies focus on the wheel-rail adhesion coefficient values and variation patterns under different medium conditions,without considering whether the rail surface with different medium can provide sufficient traction/braking utilized adhesion coefficient for the train.Therefore,there is a risk of traction overspeeding/braking skidding.This study analyzes whether the rail surface with different medium can provide sufficient traction/braking utilized adhesion coefficient for the train and whether there is redundancy.Based on these findings,relevant measures for the reasonable and optimized utilization of adhesion are derived to further ensure operation safety of the train.

High Moments Jarque-Bera Tests for Arbitrary Distribution Functions

The Jarque-Bera’s fitting test for normality is a celebrated and powerful one. In this paper, we consider general Jarque-Bera tests for any distribution function (df) having at least 4k finite moments for k ≥ 2. The tests use as many moments as possible whereas the JB classical test is supposed to test only skewness and kurtosis for normal variates. But our results unveil the relations between the coeffients in the JB classical test and the moments, showing that it really depends on the first eight moments. This is a new explanation for the powerfulness of such tests. General Chi-square tests for an arbitrary model, not only normal, are also derived. We make use of the modern functional empirical processes approach that makes it easier to handle statistics based on the high moments and allows the generalization of the JB test both in the number of involved moments and in the underlying distribution. Simulation studies are provided and comparison cases with the Kolmogorov-Smirnov’s tests and the classical JB test are given.

A Practical Guide to Statistical Tests in the Biomedical Field: From Parametric to Nonparametric, Where and How?

Healthcare decisions are based on scientific evidence obtained from medical studies by gathering data and analyzing it to obtain the best results. When analyzing data, biostatistics is a powerful tool, but healthcare professionals lack knowledge in this field. This lack of knowledge can manifest itself in situations such as choosing the wrong statistical test for the right situation or applying a statistical test without checking its assumptions, leading to inaccurate results and misleading conclusions. With the help of this “narrative review”, the aim is to bring biostatistics closer to healthcare professionals by answering certain questions: how to describe the distribution of data? how to assess the normality of data? how to transform data? and how to choose between nonparametric and parametric tests? Through this work, our hope is that the reader will be able to choose the right test for the right situation, in order to obtain the most accurate results.

A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.

A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.

Analysis of inhibition of concrete steel-rebar corrosion by Na_2Cr_2O_7 concentrations:Implications for conflicting reports on inhibitor effectiveness

Corrosion test data were measured using non-destructive electrochemical techniques and analysed for studying inhibition effectiveness by different concentrations of NazCr207 on the corrosion of concrete steel-rehar in NaC1 and in H2SO4 media. For these, specifications of ASTM G16-95 R04 were combined with the normal and the Gumbel probability density functions as model analytical methods for addressing issues of conflicting reports of inhibitor effectiveness that had generated concerns. Results show that reinforced concrete samples admixed with concentrations having 4 g （0.012 7 tool）, 8 g （0.025 4 mol） and 6 g （0.019 l tool） NaaCr207 exhibited, in that order, high inhibition effectiveness, with respective efficiency, r/, of （90.46±1.30）%, （88.41＋2.24）% and （84.87±4.74）%, in the NaC1 medium. These exhibit good agreements within replicates and statistical methods for the samples. Also, optimal inhibition effectiveness model in the H2SO4 medium was exhibited by 8 g （0.025 4 mol） Na2Cr207 concentration having r/=（78.44±1.10）%. These bear implications for addressing conflicting test data in the study of effective inhibitors for mitigating steel-rebar corrosion in aggressive environments.

Initial Stable State of Ocean Floor Deposits

Extensive oedometer tests and physical tests have been conducted on remolded and reconstituted marine soils with different initial water contents and liquid limits. The oedometer test data can be well fitted with a straight line in the bilogarithmic ln(1+ e ) ～ lg p plot. The initial effective stress corresponding to the initial void ratio is determined by extrapolation of the bilogarithmic compression line. This new way of extrapolating oedometer test data to the initial void ratio overcomes the difficulty of measuring the residual effective stress of soils in the remolded state. The initial stable compression line of ocean floor deposits under different deposition environments corresponds to the compression line at the sensitivity equal to one. This initial stable compression line obtained in this study is consistent with the available compression line at the sensitivity equal to one which is proposed based on the experimental data of remolded undrained strength and the theoretical concept of Cam clay critical state line.

引入相量算子和流向算子的天鹰优化算法

针对天鹰优化算法搜索效率不足,容易陷入局部最优的缺点,提出多策略改进天鹰优化算法(MIAO).引入广义正态分布优化算法(GNDO),将该算法得出的结果与天鹰优化算法第1阶段得出的结果进行比较,筛选出这2种优化算法下的最优值.该操作扩大了搜索空间,提高了解的质量.引入相量算子,将第2阶段变为自适应的非参数优化,提高算法的高维优化能力.针对天鹰优化算法在迭代后期存在种群多样性降低、局部开发能力不足的问题,在天鹰算法的第3阶段引入流向算子,使信息可以在每个个体间相互传递,提高种群信息的利用率,增强天鹰优化算法的开发性能.通过对16个测试函数寻优对比分析以及Wilcoxon秩和检验可知,MIAO的寻优能力和收敛速度都有较大的提升.为了验证MIAO算法的实用性和可行性,采用所提算法求解减速器设计问题,通过实际工程优化问题的实验对比分析可知,MIAO算法在处理现实优化问题上具有一定的优越性.

二项分布双边收尾概率和假设检验统计量的几处修正

二项分布是广泛存在的一种离散型概率分布。服从二项分布B(n,p)的一个随机变量等于n个相互独立且服从贝努利分布B(1,p)的随机变量之和,二项分布包含参数p的估计与检验等同于贝努利分布参数p的估计与检验。本文修正常见教科书中有关二项分布双边收尾概率计算和假设检验统计量构建中存在的3处问题。(1)对二项分布B(n,p)的取值概率pk(k=0,1,…,n)从小到大排序,排序后的概率用p_((k))表示,观测值k的双边收尾精确概率等于■;(2)二项分布B(n,p)参数p与给定值p0的差异显著性检验统计量被修正为■,该统计量在大样本条件下近似服从正态分布N(p–p0,1);(3)二项分布B(n1,p1)和B(n2,p2)的参数p1和p2差异显著性检验统计量被修正为■,该统计量在大样本条件下近似服从正态分布N(p1–p2,1)。修正后的双边收尾概率是精确值,不会出现概率大于1的问题。修正后的2个检验统计量无论原假设是否成立,其大样本近似正态分布的方差均为1,有利于准确研究备择假设条件下检验统计量的功效。此外,文中还介绍了小样本条件下二项分布参数的精确检验,对比分析了准确检验与近似检验的异同;讨论了修正统计量的理论基础,给出了小概率和大样本的判定标准,列出了贝努利分布参数检验与正态分布均值检验的异同。期望读者能够从中了解到假设检验与统计推断作为统计学核心研究内容的全貌。

Minitab数据分析在烟煤黏结指数测定中的应用

阐述了全自动黏结指数搅拌仪的使用过程中常常出现一些问题,导致烟煤黏结指数测定结果常常出现偏差。应用Minitab软件中的正态性分布检验、描述性统计分析、等方差检验、等价检验等方法对烟煤黏结指数测定中采用机械搅拌煤样后的数据超差问题进行具体分析,并通过增加人工搅拌解决此类问题。

燃料电池预测模型输出结果统计分析

基于神经网络算法建立的燃料电池寿命预测模型,输出结果都因随机性存在不确定的问题,即每次预测的输出结果都不同。针对此问题,基于长短时记忆(LSTM)神经网络算法建立燃料电池寿命预测模型,多次运行试验样本数据,利用统计学方法对输出结果的分布规律进行统计特性分析,发现基于LSTM神经网络的寿命预测模型,输出结果符合正态分布规律。根据此结论,可采用多次平均结果作为燃料电池寿命预测模型的输出结果,以提升输出结果的预测精度及稳定性。

基于正态曲线和有效积温的美国白蛾发生预测和除治效果评估机制研究

经拟合,美国白蛾成虫羽化符合正态分布。求算出成虫-成虫高峰日有效积温常数为877.6±84.3日度、当年成虫高峰日有效积温常数309.3±31.5日度,并给出了通过高峰日有效积温和成虫种群消长趋势指数进行当代和下一代成虫数量预测的方法。在全种群治理理念的指导下,提出了空间覆盖量和种群覆盖量的概念,并在此基础上制定了一套幼虫种群死亡量计算方法,其可靠性在对往年飞防除治实践中得到了验证。

一种有雾天气图像景物影像的清晰化方法

针对雾天下拍摄图像的退化现象 ,提出了一种景物影像清晰化的方法。该方法不需要依据大气模型 ,即可直接对景物的细节信息进行增强处理 ,并可用移动模板对不同深度的场景进行分割 ,以对模板中的区域进行块重叠直方图均衡化处理。为了能在对景物细节信息进行增强的同时 ,避免天空噪声的影响 ,可根据图像的灰度分布特性 ,求出天空区域灰度的最佳近似正态分布 ,再由这个近似正态分布估计来得到分割天空区域的灰度值分布范围 ,以增强景物细节信息。实验结果表明 。

角尺度判断林木水平分布格局的新方法

【目的】提出角尺度判断林木水平分布格局的检验方法,以期进一步完善角尺度判断林木水平分布格局理论。【方法】采用林分空间结构分析软件Winkelmass模拟产生面积为70 m×70 m、不同密度、不同水平分布格局的模拟林分6 000个,东北阔叶红松林实测林分2个,验证新方法判断林木水平分布格局的准确性,并与聚集指数R及Ripley’s L判断结果进行比较。【结果】依据随机分布林分角尺度均值(W-)符合正态分布的结论及其与标准差的关系,提出通过正态分布检验林分(树种)平均角尺度判断林木水平分布格局的方法。运用正态分布检验林分(树种)平均角尺度的方法判断林木水平分布格局结果与模拟林分水平分布格局的符合率达到了100%,而运用聚集指数R显著性检验判断林木水平分布格局结果的符合率则随着林分密度的增加而增加;面积为70 m×70 m、密度为50株·hm-2时不同水平分布格局的模拟林分判断结果表明,通过正态分布检验林分(树种)平均角尺度判断林木水平分布格局方法不受林木间的距离影响,而相邻单株之间的平均距离是影响聚集指数R判断林木水平分布格局结果的关键因素。甘肃小陇山松栎混交林每木定位数据和吉林蛟河阔叶红松林每木定位数据判断结果表明,在置信水平α为0.05时,新方法对松栎混交林的判断结果与Ripley’s L函数点格局分析方法判断结果一致,对阔叶红松林中水曲柳和红松种群水平分布格局判断为随机分布,对林分及其他树种水平分布格局的判断结果与Ripley’s L函数一致;而聚集指数R则将松栎混交林中的华山松水平分布格局判断为随机分布,将阔叶红松全林的水平分布格局判断为聚集分布,核桃楸的水平分布格局判断为随机分布;在置信水平α为0.1时,正态分布检验林分(树种)平均角尺度判断林木水平分布格局方法对2个林分/种群的判断结果与Ripley’s L函数点格局分析方法判断结果完全一致,而聚集指数R与Ripley’s L检验的判断结果的差别明显增加,说明置信水平对水平分布格局判断结果影响比较明显。【结论】研究提出的正态分布检验林分(树种)平均角尺度判断林木水平分布格局的方法克服了统一的置信区间不适用于评判抽样调查或群落中数量较少的种群水平分布格局问题,进一步完善了角尺度判断林木水平分布格局理论,提升了角尺度判断林木水平分布格局的准确性与适用范围。