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.

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.

Association between people’s attitudes towards human-elephant conflict and their locational,demographic,and socio-economic characteristics in Buxa Tiger Reserve and its adjoining area,India

“Human-elephant conflict(HEC)”,the alarming issue,in present day context has attracted the attention of environmentalists and policy makers.The rising conflict between human beings and wild elephants is common in Buxa Tiger Reserve(BTR)and its adjoining area in West Bengal State,India,making the area volatile.People’s attitudes towards elephant conservation activity are very crucial to get rid of HEC,because people’s proximity with wild elephants’habitat can trigger the occurrence of HEC.The aim of this study is to conduct an in-depth investigation about the association of people’s attitudes towards HEC with their locational,demographic,and socio-economic characteristics in BTR and its adjoining area by using Pearson’s bivariate chi-square test and binary logistic regression analysis.BTR is one of the constituent parts of Eastern Doors Elephant Reserve(EDER).We interviewed 500 respondents to understand their perceptions to HEC and investigated their locational,demographic,and socio-economic characteristics including location of village,gender,age,ethnicity,religion,caste,poverty level,education level,primary occupation,secondary occupation,household type,and source of firewood.The results indicate that respondents who are living in enclave forest villages(EFVs),peripheral forest villages(PFVs),corridor village(CVs),or forest and corridor villages(FCVs),mainly males,at the age of 18–48 years old,engaged with agriculture occupation,and living in kancha and mixed houses,have more likelihood to witness HEC.Besides,respondents who are illiterate or at primary education level are more likely to regard elephant as a main problematic animal around their villages and refuse to participate in elephant conservation activity.For the sake of a sustainable environment for both human beings and wildlife,people’s attitudes towards elephants must be friendly in a more prudent way,so that the two communities can live in harmony.

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.

A Note on Cochran Test for Homogeneity in Two Ways ANOVA and Meta-Analysis

In this paper, we generalize the proof of the Cochran statistic in the case of an ANOVA two ways structure that asymptotically follows a Chi-2. While construction of homogeneity statistics test usually resorts to the determination of the covariance matrix and its inverse, the Moore-Penrose matrix, our approach, avoids this step. We also show that the Cochran statistic in ANOVA two ways is equivalent to conventional homogeneity statistics test. In particular, we show that it satisfies the invariance property. Finally, we conduct empirical verification from a meta-analysis that confirms our theoretical results.

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.

HIV Testing Decision and Determining Factors in Ghana

Knowledge on individual’s HIV/AIDS status provides a tool to reduce or avoid HIV transmission, spread and mortalities due to HIV-related illness. However, most people still do not know their HIV status because they are not willing to test for HIV/AIDS due to various reasons. Hence the aim of this paper is to investigate the effects of various risk factors that are likely to influence decision to ever test for HIV/AIDS. The data used in this paper were obtained from the Ghana Demographic and Health Survey (n = 1828 observations and 32 risk factors). We applied the Chi-Square test statistic and the logistic regression model to the data in order to study the effects of these risk factors on one’s decision to ever test for HIV. STATA version 14.1 and R version 3.5.2 were used to carry out the statistical analyses. Generally, the results show that education, especially higher education significantly (OR = 0.53, 95% = 0.230, 0.837) increases the likelihood to ever test for HIV. Also, the younger the age groups the higher the effect and significance in the likelihood to ever test for HIV. We found that HIV-TB co-infection (OR = 0.53, 95% = 0.165, 0.893), use of condom anytime one has sex (OR = 0.31, 95% = 0.054, 0.573), wealth index (OR = 0.46, 95% = 0.137, 0.791), awareness of HIV transmission during child-delivery, number of partners significantly affect HIV testing. Those with many partners are less likely (OR = -0.26, 95% = -0.504, -0.007) to ever test for HIV and those who know that healthy person may have HIV are more likely (OR = 0.41, 95% = 0.137, 0.679) to ever test for HIV. Age is the common significant risk factor of ever tested for HIV across the 10 regions in Ghana. Resources should be allocated for more education on these significant risk factors in order to help in the fight against HIV-Health related issues.

On the Different Ways to Handle the Trend of Disease Risk in Genetic Association Tests

Genetic association studies usually apply the simple chi-square (χ2)-test for testing association between a single-nucleotide polymorphism (SNP) and a particular phenotype, assuming the genotypes and phenotypes are independent. So, the conventional χ2-test does not consider the increased risk of an individual carrying the increasing number of disease responsible allele (a particular genotype). But, the association tests should be performed with the consideration of this disease risk according to the mode of inheritance (additive, dominant, recessive). Practical demonstration of the two possible methods for considering such order or trends in contingency tables of genetic association studies using SNP genotype data is the purpose of this paper. One method is by pooling the genotypes, and the other is scoring the individual genotypes, based on the disease risk according to the inheritance pattern. The results show that the p-values obtained from both the methods are similar for the dominant and recessive models. The other important features of the methods were also extracted using the SNP genotype data for different inheritance patterns.

Correlation knowledge extraction based on data mining for distribution network planning

Traditional distribution network planning relies on the professional knowledge of planners,especially when analyzing the correlations between the problems existing in the network and the crucial influencing factors.The inherent laws reflected by the historical data of the distribution network are ignored,which affects the objectivity of the planning scheme.In this study,to improve the efficiency and accuracy of distribution network planning,the characteristics of distribution network data were extracted using a data-mining technique,and correlation knowledge of existing problems in the network was obtained.A data-mining model based on correlation rules was established.The inputs of the model were the electrical characteristic indices screened using the gray correlation method.The Apriori algorithm was used to extract correlation knowledge from the operational data of the distribution network and obtain strong correlation rules.Degree of promotion and chi-square tests were used to verify the rationality of the strong correlation rules of the model output.In this study,the correlation relationship between heavy load or overload problems of distribution network feeders in different regions and related characteristic indices was determined,and the confidence of the correlation rules was obtained.These results can provide an effective basis for the formulation of a distribution network planning scheme.

Agricultural Market Name Geo-Locating System Based on an Administrative Ontology and Web Search Engine

The problem of associating the agricultural market names on web sites with their locations is essential for geographical analysis of the agricultural products. In this paper, an algorithm which employs the administrative ontology and the statistics from the search results were proposed. The experiments with 100 market names collected from web sites were conducted. The experimental results demonstrate that the algorithm proposed obtains satisfactory performance in resolving the problem above, thus the effectiveness of the method is verified.

Simulated Minimum Hellinger Distance Inference Methods for Count Data

In this paper, we consider simulated minimum Hellinger distance (SMHD) inferences for count data. We consider grouped and ungrouped data and emphasize SMHD methods. The approaches extend the methods based on the deterministic version of Hellinger distance for count data. The methods are general, it only requires that random samples from the discrete parametric family can be drawn and can be used as alternative methods to estimation using probability generating function (pgf) or methods based matching moments. Whereas this paper focuses on count data, goodness of fit tests based on simulated Hellinger distance can also be applied for testing goodness of fit for continuous distributions when continuous observations are grouped into intervals like in the case of the traditional Pearson’s statistics. Asymptotic properties of the SMHD methods are studied and the methods appear to preserve the properties of having good efficiency and robustness of the deterministic version.

Usability perceptions and beliefs about smart thermostats by chi-square test, signal detection theory, and fuzzy detection theory in regions of Mexico

It is well known that smart thermostats (STs) have become key devices in the implementation of smart homes;thus, they are considered as primary elements for the control of electrical energy consumption in households. Moreover, energy consumption is drastically affected when the end users select unsuitable STs or when they do not use the STs correctly. Furthermore, in future, Mexico will face serious electrical energy challenges that can be considerably resolved if the end users operate the STs in a correct manner. Hence, it is important to carry out an in-depth study and analysis on thermostats, by focusing on social aspects that influence the technological use and performance of the thermostats. This paper proposes the use of a signal detection theory (SDT), fuzzy detection theory (FDT), and chi-square (CS) test in order to understand the perceptions and beliefs of end users about the use of STs in Mexico. This paper extensively shows the perceptions and beliefs about the selected thermostats in Mexico. Besides, it presents an in-depth discussion on the cognitive perceptions and beliefs of end users. Moreover, it shows why the expectations of the end users about STs are not met. It also promotes the technological and social development of STs such that they are relatively more accepted in complex electrical grids such as smart grids.

Current Situation of College Students’ Entrepreneurship and Employment in the Countryside in the Context of Rural Revitalization

Focusing on the talent training in the strategy of revitalizing the countryside, this paper uses questionnaire survey, field survey, descriptive statistics, chi-square test and other methods to study the willingness of college students to "go to the countryside" to contribute to rural development after graduation, as well as the influencing factors. The results show that the willingness of college students to "go to the countryside" is negative after graduation, and engaging in rural education and returning to their hometown to start a business is the mainstream will of college students to "go to the countryside". The one-sidedness of the understanding of rural areas, less employment opportunities, low wages, poor infrastructure conditions and the views of the older generation are the important reasons that hinder college students from "going to the countryside". The good environment in rural areas and the guidance of policies are the biggest promoting factors for "going to the countryside". The willingness of rural college students to "go to the countryside" is significantly higher than that of urban college students. The freshman s willingness to "go to the countryside" is the most positive, and the graduate students willingness to "go to the countryside" is the most negative. The college students majoring in agriculture are most willing to support the development of rural areas, while the students of "medicine","literature" and "art" are most unwilling to "go to the countryside". Whether or not to participate in the "volunteer activities for the country people" has no impact on the willingness to "go to the countryside".

Destructive and Nondestructive Determination of ²²⁶Ra and ²²⁸Ra in Drinking Water by Gamma Spectrometry

The Safe Drinking Water Act (SDWA) mandates that the drinking water should be monitored for 226Ra and 228Ra isotopes and establishes the Maximum Contaminant Level of 185 mBq/L (5 pCi·L-1) for the sum. In addition, SDWA regulates the Detection Limit (DL) of 37.0 mBq/L (1 pCi/L) for each isotope. The purpose of this work is to develop a working method for the determination of radium isotopes in drinking water satisfying the regulatory requirements of U.S. Environmental Protection Agency by utilizing our extensive experience in low-background gamma spectrometry at this laboratory. Two versions of the method were studied: destructive and non-destructive. Destructive method used the BaSO4 coprecipitation as well as 133Ba tracer for chemical recovery. We have used three gamma spectrometers: low-background 102% and 134% efficient with top muon guards, as well as an ultralow-background 140% efficient with full muon guard. We obtained a range of DLs from 5.3 to 22.6 mBq/L for 226Ra and from 7.4 to 30.4 mBq/L for 228Ra using the destructive method. For non-destructive method, the DL range was 26.0 to 26.9 mBq/L for 226Ra and 27.6 to 28.6 mBq/L for 228Ra using the 140% detector. To verify the methods, 7 to 10 laboratory control samples were spiked with both 226Ra and 228Ra at two different activities of 37.0 and 185 mBq/L. The results were evaluated by performing a combined location/variance chi-square test at a right-tail significance of 0.01 (99% Confidence Level), as stipulated by EPA. The verification results passed the chi-square tests at both activity levels. The destructive method can be accomplished using low-background gamma spectrometry, whereas non-destructive method requires ultralow-background gamma spectrometry.

Likelihood and Quadratic Distance Methods for the Generalized Asymmetric Laplace Distribution for Financial Data

Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models.

Using Markov chains to predict the natural progression of diabetic retinopathy

AIM: To study the natural progression of diabetic retinopathy in patients with type 2 diabetes.METHODS: This was an observational study of 153 cases with type 2 diabetes from 2010 to 2013. The state of patient was noted at end of each year and transition matrices were developed to model movement between years. Patients who progressed to severe non-proliferative diabetic retinopathy(NPDR) were treated.Markov Chains and Chi-square test were used for statistical analysis.RESULTS: We modelled the transition of 153 patients from NPDR to blindness on an annual basis. At the end of year 3, we compared results from the Markov model versus actual data. The results from Chi-square test confirmed that there was statistically no significant difference(P =0.70) which provided assurance that the model was robust to estimate mean sojourn times. The key finding was that a patient entering the system in mild NPDR state is expected to stay in that state for 5y followed by 1.07 y in moderate NPDR, be in the severe NPDR state for 1.33 y before moving into PDR for roughly8 y. It is therefore expected that such a patient entering the model in a state of mild NPDR will enter blindness after 15.29 y.CONCLUSION: Patients stay for long time periods in mild NPDR before transitioning into moderate NPDR.However, they move rapidly from moderate NPDR to proliferative diabetic retinopathy(PDR) and stay in that state for long periods before transitioning into blindness.

Exchange Rate Market Sentiment Analysis of Major Global Currencies

The paper deals with the analysis of market sentiments in exchange rates which are of great interest to trading individuals and institutional investors. For example, an institutional investor or a trading individual makes better investments and minimizes losses when equipped with an understanding of market sentiments in weekly or monthly exchange returns. In the approach suggested here, a typical market sentiment is defined on the basis of the certain function of the mean and the standard error of the logarithm of the ratio of successive daily exchange rates. Based on this surmise, the market sentiments are classified into various states, whereby states are defined according to the perceptions of the market player. A multinomial probability model is built to capture the uncertainties in market sentiments. Two asymptotically distribution-free tests, namely the chi-square and the likelihood ratio test of goodness of fit for the hypothesis of the symmetry in market sentiments are suggested. Two different measures of market sentiments are proposed. The approach advocated here will be of interest to researchers, exchange rate traders and financial analysts. As an application of the proposed line of approach, we analyze weekly market sentiments that govern exchange rates of the major global currencies—EUR, GBP, SDR, YEN, ZAR, USD, data from 2001-2012. Some interesting conclusions are revealed based on the data analysis.