Potential applications of rapid/elementary nonparametric statistical techniques (NST) to electrochemical problems

A major advantage of NST lies in the unimportance of the probability distribution of observations. In this paper, the sign test, the rank-sum test, the Kruskal-Wallis test, the Friedman test, and the runs test illustrate the potential of certain rapid NST for the evaluation of electrochemical process performance.     

Weibull Statistics in Dielectric Strength of Oil-impregnated Pressboard under Ramped AC and DC Voltages

AC and DC breakdown tests were performed on large populations of oil-impregnated pressboard samples. The effect of voltage ramp rate on dielectric strength has been investigated. A statistical analysis of breakdown data was carried out using the Weibull distribution. The 90% confidence intervals of Weibull graphs were calculated. The study shows that dielectric strength and shape parameter change versus ramp rate. The variations are attributed to the size and number of defects. Discharges occur from the oil to the oil-pressboard interface and lead to breakdown. DC dielectric strength is larger than that corresponding to AC voltage. This is ascribed to the dissipated energy difference under the two types of field and the fatigue produced by the alternating voltage. This phenomenon is related to space charge. Under DC stress, dielectric strength is higher under negative polarity. It is assigned to the different quantities of space charge accumulated under the two polarities.     

Extreme quantile estimation using order statistics with minimum cross-entropy principle

The paper presents a general approach to the estimation of the quantile function of a non-negative random variable using the principle of minimum cross-entropy (CrossEnt) subject to constraints specified in terms of expectations of order statistics estimated from observed data.Traditionally CrossEnt is used for estimating the probability density function under specified moment constraints. In such analyses, consideration of higher order moments is important for accurate modelling of the distribution tail. Since the higher order (>2) moment estimates from a small sample of data tend to be highly biased and uncertain, the use of CrossEnt quantile estimates in extreme value analysis is fairly limited.The present paper is an attempt to overcome this problem via the use of probability weighted moments (PWMs), which are essentially the expectations of order statistics. In contrast with ordinary statistical moments, higher order PWMs can be accurately estimated from small samples. By interpreting a PWM as the moment of quantile function, the paper derives an analytical form of quantile function using the CrossEnt principle. Monte Carlo simulations are performed to assess the accuracy of CrossEnt quantile estimates obtained from small samples.     

干旱区水量平衡模型参数率定策略研究

以干旱区水量平衡模型为研究对象,建立了模型参数分区率定策略,采用改进的动尺度搜索算法(MDDS)对模型中河段水量损失系数、灌区退水系数等参数进行率定。使用条件概率和贝叶斯统计理论论证了分区率定策略的理论可行性,并通过干旱区(新疆开都河)水量平衡模型对模型参数全区和分区率定策略的性能优劣进行实例验证。利用焉耆站2000年1月—2015年12月的实测月平均流量过程和宝浪苏木闸2000年1月—2009年12月的实测月平均流量过程分别对水量平衡模型的焉耆站模拟结果与宝浪苏木站模拟结果进行参数率定,并对率定结果进行了分析。应用于新疆开都河流域焉耆站、宝浪苏木站的模拟结果表明,分区率定在每个分区的待率定参数个数、计算时间和率定效果方面较全区率定有较大优势。     

Assessing Local Model Adequacy in Bayesian Hierarchical Models Using the Partitioned Deviance Information Criterion

Many diagnostic tools and goodness-of-fit measures, such as the Akaike information criterion (AIC) and the Bayesian deviance information criterion (DIC), are available to evaluate the overall adequacy of linear regression models. In addition, visually assessing adequacy in models has become an essential part of any regression analysis. In this paper, we focus on a spatial consideration of the local DIC measure for model selection and goodness-of-fit evaluation. We use a partitioning of the DIC into the local DIC, leverage, and deviance residuals to assess the local model fit and influence for both individual observations and groups of observations in a Bayesian framework. We use visualization of the local DIC and differences in local DIC between models to assist in model selection and to visualize the global and local impacts of adding covariates or model parameters. We demonstrate the utility of the local DIC in assessing model adequacy using HIV prevalence data from pregnant women in the Butare province of Rwanda during the period 1989-1993 using a range of linear model specifications, from global effects only to spatially varying coefficient models, and a set of covariates related to sexual behavior. Results of applying the diagnostic visualization approach include more refined model selection and greater understanding of the models as applied to the data.     

Sterols and triterpene diols in olive oil as indicators of variety and degree of ripening

Sterols and triterpene diols in olive oil as indicators of variety and degree of ripening derived from three olive varieties and produced at three different harvesting periods were studied. In order to test the stability of the proposed indicators, oils obtained were stored for 12 months at three different temperatures. Thirty-six samples in total were subjected to GC analysis and results were processed by multivariate chemometric methods (MANOVA, PCA, and SLDA). Campesterol, β-sitosterol, Δ⁷-campesterol/Δ^5,24-stigmastadienol, clerosterol, uvaol, and campestanol/Δ⁷-avenasterol were established as the indicators of variety of fresh oils, while when stored oils were included in the model, the final three compounds were substituted by 24-methylene-cholesterol/stigmasterol. The most important variables for differentiating fresh oils according to degree of ripening were Δ⁷-campesterol/β-sitosterol, uvaol/stigmasterol, clerosterol/Δ⁵-avenasterol and sitostanol/uvaol, while stored oils were differentiated by campestanol/stigmasterol, erythrodiol, stigmasterol/Δ⁷-campesterol, Δ⁵-avenasterol, 24-methylene-cholesterol/β-sitosterol and 24-methylene-cholesterol. Results demonstrated that sterols and triterpene diols can be used as indicators of variety and degree of ripening among virgin olive oils.     

工程金属材料线膨胀系数的计算

对优质碳素结构钢和几类低合金结构钢，在现有实验数据的基础上，通过迭代分离，综合统计，图象分析和数学拟合，得出按钢的主要化学成分确定其线膨胀系数的计算关系。此外，对不锈耐酸钢的线膨胀系数也建立了计算式。     

机身壁板LBW结构DFR值试验测定及理论计算[KH-*1]

飞机机身壁板是疲劳的关键位置, 空客公司首先在飞机机身壁板采用激光焊接(LBW)结构代替传统铆接结构.为评价该激光焊接结构的疲劳性能, 结合试验测定和统计学理论计算两种方法, 对两组新型铝锂合金2060-T3激光焊接焊后热处理(PWHT, 即焊后固溶+时效热处理和焊后时效热处理)结构进行疲劳试验、断口分析及细节疲劳额定强度(DFR值)分析, 分别计算了试验测定DFR值和理论DFR值.分析结果表明, 试验测定焊后固溶+时效热处理激光焊接结构的DFR值为118.0 MPa, 焊后时效热处理的DFR值为113.7 MPa, 理论DFR值分别为115.8 MPa(误差为1.86%)和112.2 MPa(误差为1.32%); 两组结构均在焊趾处产生裂纹源, 裂纹沿板材厚度方向进行扩展, 裂纹扩展区均表现为脆性解理河流花样, 不同的是前者瞬断区为微孔聚集型断裂, 断口存在大量微小韧窝, 后者瞬断区为沿晶断裂, 断口存在大量晶粒; 采用统计学理论计算, 可以较好地还原威布尔分布的形状参数, 验证了统计学理论分析方法的工程适用性, 为机身壁板LBW结构的DFR值测定提供了参考依据.     

Time series analysis based on running Mann‐Whitney Z Statistics

A time series analysis method based on the calculation of Mann–Whitney U statistics is described. This method samples data rankings over running time windows, converts those samples to Mann–Whitney U statistics, and then normalizes the U statistics to Z statistics using Monte‐Carlo generated null parameters. Based on the Z statistics’ magnitudes this algorithm can identify time windows containing significant incidences of low or high data rankings, where the window length is determined by the sample size. By repeating this process with sampling windows of varying duration ranking regimes of arbitrary onset and duration can be objectively identified in a time series. The simplicity of the procedure's output – a time series’ most significant non‐overlapping ranking sequences – makes it possible to graphically identify common temporal breakpoints and patterns of variability in the analyses of multiple time series. This approach is demonstrated using United States annual temperature data during 1896–2008.