Auto-selection order of Markov chain for background sequences with chi-square test

Modeling non coding background sequences appropriately is important for the detection of regulatory elements from DNA sequences. Based on the chi square statistic test, some explanations about why to choose higher order Markov chain model and how to automatically select the proper order are given in this paper. The chi square test is first run on synthetic data sets to show that it can efficiently find the proper order of Markov chain. Using chi square test, distinct higher order context dependences inherent in ten sets of sequences of yeast S.cerevisiae from other literature have been found. So the Markov chain with higher order would be more suitable for modeling the non coding background sequences than an independent model.

大锻件统计学Chi-square test的研究和应用

根据大锻件生产的特点和统计学的基本理论方法,首次深入浅出地论述了大锻件的Chi-square test,即X2检验,并给出了具体应用示例。该方法可用于大锻件工艺参数的科学分析和生产验证,可用于大锻件质量分析和判断,可帮助逐步建立起大锻件的工序能力,帮助实现稳定并提升大锻件工艺和质量控制水平。

Large Deviations and Moderate Deviations for the Chi-Square Test in Type Ⅱ Error

We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.

Stability monitoring and evaluation of the modeled test square for prehistoric earthen sites during excavation period

In order to explore the stability of test square during archaeological excavation for prehistoric earthen sites in Hangzhou, a modeled test square with 2. 3 min depth, inplane dimensions of 5 min width by 5 m in length, and an archaeological column in the middle was excavated by means of a top-down excavation technique. To investigate the stability performance of the modeled test square and the associated effect on the adjacent area, a real-time comprehensive instrumentation program was conducted during the excavation. Field observations included ground settlements, lateral displacement, pore pressure and underground water level. Monitoring data indicates that the ground settlement induced by dewatering and unloading action basically decreases with the increase of the distance away from the pit edge, and the lateral displacements at four sides showa nonlinear variation along the depth. The maximum value is far below the acceptable value regulated by the related standard,which validates the stability of the modeled test square during excavation. Variations of pore pressure and water level suggest that long-term stability should be paid more attention due to the slowconsolidation of soft soil. Meanwhile, it is proved that the step shape of the wall can resist lateral displacement more effectively than the vertical shape of wall. This case study provides insights into the real archaeological excavation in Hangzhou, in particular Liangzhu prehistoric earthen sites.

Use of Pearson’s Chi-Square for Testing Equality of Percentile Profiles across Multiple Populations

In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For example, it may be more informative to compare two or more populations with respect to their within population distributions by testing the hypothesis that their corresponding respective 10th, 50th, and 90th percentiles are equal. As a generalization of the median test, the proposed test statistic is asymptotically distributed as Chi-square with degrees of freedom dependent upon the number of percentiles tested and constraints of the null hypothesis. Results from simulation studies are used to validate the nominal 0.05 significance level under the null hypothesis, and asymptotic power properties that are suitable for testing equality of percentile profiles against selected profile discrepancies for a variety of underlying distributions. A pragmatic example is provided to illustrate the comparison of the percentile profiles for four body mass index distributions.

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.

基于Chi-square检验的分布式网络入侵检测系统

针对网络攻击的新特点,本文提出了一种基于Chi-square检验的分布式网络入侵检测系统模型CTDIDS。设计并实现了一个基于异常检测的入侵分析引擎。通过对网络数据包的分析,运用Chi-square值比较对系统的行为进行检测。与现有的入侵检测方法相比,本文提出的方法具有更好的环境适应性和数据协同分析能力。实验证明,分布式入侵检测系统CTDIDS具有更高的准确性和扩展性。

Numerical simulation of the behaviors of test square for prehistoric earthen sites during archaeological excavation

During the process of archaeological excavation in the regions of Southeast China, collapse of test square usually occurs due to poor site-specific conditions. In this paper, the fast Lagrangian analysis of continua in three dimensions（FLAC3D） is employed to reveal the behaviors of test square. Taking the archaeological works in Liangzhu prehistoric earthen sites as the research background, the paper first introduces the geological setting, excavation procedure and monitoring scheme of the studied test square. Then, the deformation of four sides of the test square is modeled using FLAC3D. By comparison, it shows that the numerical results are consistent with the results from field monitoring. The result suggests that the numerical simulation can be effectively applied to representing the actual behaviors of the test square,which is helpful for determination of excavation scheme and stability evaluation of the test square during archaeological excavation.

Constant Stress Accelerated Life Tests for Vacuum Fluorescent Display Based on Least Square Method

To estimate the life of vacuum fluorescent display （VFD） more accurately and reduce test time and cost, four constant stress accelerated life tests （CSALTs） were conducted on an accelerated life test model. In the model, statistical analysis of test data is achieved by applying lognormal function to describe the life distribution, and least square method （LSM） to calculate the mean value and the standard deviation of logarithm. As a result, the accelerated life equation was obtained, and then a self-developed software was developed to predict the VFD life. The data analysis results demonstrate that the VFD life submits to lognormal distribution, that the accelerated model meets the linear Arrhenius equation, and that the precise accelerated parameter makes it possible to acquire the life information of VFD within one month.

Chi-Square Distribution: New Derivations and Environmental Application

We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.

WEIGHTED LEAST SQUARE METHOD FOR S-N CURVE FITTING

An S-N curve fitting approach is proposed based on the weighted least square method, and the weights are inversely proportional to the length of mean confidence intervals of experimental data sets. The assumption coincides with the physical characteristics of the fatigue life scatter. Two examples demonstrate the method. It is shown that the method has better accuracy and reasonableness compared with the usual least square method.

Improving Middle Square Method RNG Using Chaotic Map

One of the classic approaches in PRNGs is the middle square method in which with a simple mathe-matical model generating pseudorandom numbers in high speed and minimum correlation between output numbers. Despite these unique characteristics, the method contains weaknesses that a broader application of this algo- rithm will face. In this paper is studied middle square method and then a logistic chaotic map is introduced with its specific features and its improved weaknesses via using these characteristics. Finally the NIST tests suite s are presented, in order to detect the specific characteristics expected from truly random sequences.

A Note on Change Point Detection Using Weighted Least Square

This paper is concerned with the application of weighted least square method in change point analysis. Testing shift in the mean normal observations with time varying variances as well as of a GARCH time series are considered. For both cases, the weighted estimators are given and their asymptotic behaviors are studied. It is also described that how the resampling methods like Monte Carlo and bootstrap may be applied to compute the finite sample behavior of estimators.

基于Chi-quare检验与词义分析的试题重复检测算法

针对无纸化考试系统入库试题重复检测问题;提出基于卡方检验与词义分析的试题重复检测算法,首先自动提取试题的特征信息词项,利用卡方检验改进公式进行特征词分析并删除冗余词;其次,结合中文WordNet词典对特征词进行词义分析,并利用Tf-Idf方法计算入库试题的特征词向量与不同题型特征词的余弦相似度;最后,根据所得相似度值判别该试题是否与题库试题重复。实验结果表明,在重复度阀值选取0.8时,算法耗时少、准确性高。

Estimation for constant-stress accelerated life test from generalized half-normal distribution

In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.

Regressive approach for predicting bearing capacity of bored piles from cone penetration test data

In this study, th e least sq u are su p p o rt v ecto r m achine （LSSVM） alg o rith m w as applied to predicting th ebearing capacity o f b ored piles e m b ed d ed in sand an d m ixed soils. Pile g eo m etry an d cone p e n e tra tio nte s t （CPT） resu lts w ere used as in p u t variables for pred ictio n o f pile bearin g capacity. The d ata u se d w erecollected from th e existing litera tu re an d consisted o f 50 case records. The application o f LSSVM w ascarried o u t by dividing th e d ata into th re e se ts： a train in g se t for learning th e pro b lem an d obtain in g arelationship b e tw e e n in p u t variables an d pile bearin g capacity, and testin g an d validation sets forevaluation o f th e predictive an d g en eralization ability o f th e o b tain ed relationship. The predictions o f pilebearing capacity by LSSVM w ere evaluated by com paring w ith ex p erim en tal d ata an d w ith th o se bytrad itio n al CPT-based m eth o d s and th e gene ex pression pro g ram m in g （GEP） m odel. It w as found th a t th eLSSVM perform s w ell w ith coefficient o f d eterm in atio n , m ean, an d sta n d ard dev iatio n equivalent to 0.99,1.03, an d 0.08, respectively, for th e testin g set, an d 1, 1.04, an d 0.11, respectively, for th e v alidation set. Thelow values o f th e calculated m ean squared e rro r an d m ean ab so lu te e rro r indicated th a t th e LSSVM w asaccurate in p redicting th e pile bearing capacity. The results o f com parison also show ed th a t th e p roposedalg o rith m p red icted th e pile bearin g capacity m ore accurately th a n th e trad itio n al m eth o d s including th eGEP m odel.

Nondestructive testing method of wood moisture content based on a planar capacitance sensor model

For our research, a new hybrid experimental-computational method is presented. We applied a least squares fitting method （LSFM） to reconstruct the wood moisture content （WMC） from the data measured with a planar capacitance sensor. A boundary element method （BEM） was used to compute the relationship between capacitance and the dielectric constant. A functional relationship between MC and the dielectric constant was identified by LSFM. The agreement of this final computation result with the experimental data indicates that this method can be used to estimate the WMC quickly and effectively with engineering analysis. Compared with popular statistical methods, a large number of experiments are avoided, some costs of testing are reduced and the efficiency of testing is enhanced.

Improvement of the Preliminary Test Estimator When Stochastic Restrictions are Available in Linear Regression Model

Ridge type estimators are used to estimate regression parameters in a multiple linear regression model when multicolinearity exists among predictor variables. When different estimators are available, preliminary test estimation procedure is adopted to select a suitable estimator. In this paper, two ridge estimators, the Stochastic Restricted Liu Estimator and Liu Estimator are combined to define a new preliminary test estimator, namely the Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE). The stochastic properties of the proposed estimator are derived, and the performance of PTSRLE is compared with SRLE in the sense of mean square error matrix (MSEM) and scalar mean square error (SMSE) for the two cases in which the stochastic restrictions are correct and not correct. Moreover the SMSE of PTSRLE based on Wald (WA), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are derived, and the performance of PTSRLE is compared using WA, LR and LM tests as a function of the shrinkage parameter d with respect to the SMSE. Finally a numerical example is given to illustrate some of the theoretical findings.

Practical integrated navigation fault detection algorithm based on sequential hypothesis testing

In detecting system fault algorithms,the false alarm rate and undectect rate generated by residual Chi-square test can affect the stability of filters.The paper proposes a fault detection algorithm based on sequential residual Chi-square test and applies to fault detection of an integrated navigation system.The simulation result shows that the algorithm can accurately detect the fault information of global positioning system（GPS）,eliminate the influence of false alarm and missed detection on filter,and enhance fault tolerance of integrated navigation systems.