PP偏度,峰度正态性检验的P-VALUES

给出了用于高维正态性检验的PP偏度,峰度及其偏度,峰度混合的检验统计量,获得了诸统计量极限分布的尾部概率展开式,由此可比较准确而迅速地获得这类检验的各种临界值及其P-Values.本文的方法也适用对其它椭球等高分布检验的P-Vlalues计算问题。

The p-value and model specification in statistics

SUMMARY The p value has been widely used as a way to summarise the significance in data analysis. However, misuse and misinterpretation of the p value is common in practice. Our result shows that if the model specification is wrong, the distribution of the p value may be inappropriate, which makes the decision based on the p value invalid.

Transient postseismic slip and aftershock triggering:A case study of the 2008 M_W7.9 Wenchuan Earthquake,China

In this study,we investigate how a stress variation generated by a fault that experiences transient postseismic slip(TPS)affects the rate of aftershocks.First,we show that the postseismic slip from Rubin-Ampuero model is a TPS that can occur on the main fault with a velocity-weakening frictional motion,that the resultant slip function is similar to the generalized Jeffreys-Lomnitz creep law,and that the TPS can be explained by a continuous creep process undergoing reloading.Second,we obtain an approximate solution based on the Helmstetter-Shaw seismicity model relating the rate of aftershocks to such TPS.For the Wenchuan sequence,we perform a numerical fitting of the cumulative number of aftershocks using the Modified Omori Law(MOL),the Dieterich model,and the specific TPS model.The fitting curves indicate that the data can be better explained by the TPS model with a B/A ratio of approximately 1.12,where A and B are the parameters in the rate-and state-dependent friction law respectively.Moreover,the p and c that appear in the MOL can be interpreted by the B/A and the critical slip distance,respectively.Because the B/A ratio in the current model is always larger than 1,the model could become a possible candidate to explain aftershock rate commonly decay as a power law with a p-value larger than 1.Finally,the influence of the background seismicity rate r on parameters is studied;the results show that except for the apparent aftershock duration,other parameters are insensitive to r.

基于熵的随机性检测相关性研究

目前,存在众多的随机性检测项目,并且许多项目都带有参数.选择所有的项目进行检测不现实,因此需要研究检测项目之间的关系.从统计学角度出发,对检测项目的相关性进行研究,首先定义了检测项目之间存在的4种关系,提出了检测项目相关度的概念,然后利用熵值法对检测项目相关度进行度量,并证明了这4种关系与相关度的联系,同时给出了一种计算相关度的算法和一个基于相关度的检测项目选择策略.所研究的结果为随机性检测项目及其参数选择提供了理论依据.与此同时,利用相关度对NIST在评选AES中所采用的检测项目进行研究,发现了其中一些检测项目之间存在着依赖关系.

随机性检测参数选择研究

从统计学角度对同一个随机性检测项目中2个独立的参数所应满足的条件进行了研究,在此基础上设计了一个假设检验方法,用于检测2个参数是否满足独立的关系。以扑克检测为实例,对其参数集中的参数进行了实验研究,并对结果进行了分析。提出的方法是一个通用的方法,可以直接应用于其他带参数的检测项目的参数关系研究中,这为随机性检测中参数选择提供了一种可操作的手段。

地理标志产品绍兴黄酒与非地理标志黄酒感官评价分析的研究

根据5位黄酒国家级评酒委员对地理标志产品绍兴黄酒与非地理标志黄酒的感官品评,对其醇和度、甜度、鲜爽度、酸度、协调性进行量化评分,采用P-value假设数据统计法进行比较分析。结果表明,绍兴地理标志黄酒产品在醇和度、鲜爽度和协调性3个方面得分均高于非绍兴地理标志黄酒产品,醇和度、鲜爽度和协调性的口感指标可以作为绍兴地理标志黄酒区别于非地理标志黄酒的特征性感官鉴定指标,为黄酒鉴别进一步研究打下基础。

Intelligent Evidence-Based Management for Data Collection and Decision-Making Using Algorithmic Randomness and Active Learning

We describe here a comprehensive framework for intelligent information management (IIM) of data collection and decision-making actions for reliable and robust event processing and recognition. This is driven by algorithmic information theory (AIT), in general, and algorithmic randomness and Kolmogorov complexity (KC), in particular. The processing and recognition tasks addressed include data discrimination and multilayer open set data categorization, change detection, data aggregation, clustering and data segmentation, data selection and link analysis, data cleaning and data revision, and prediction and identification of critical states. The unifying theme throughout the paper is that of “compression entails comprehension”, which is realized using the interrelated concepts of randomness vs. regularity and Kolmogorov complexity. The constructive and all encompassing active learning (AL) methodology, which mediates and supports the above theme, is context-driven and takes advantage of statistical learning, in general, and semi-supervised learning and transduction, in particular. Active learning employs explore and exploit actions characteristic of closed-loop control for evidence accumulation in order to revise its prediction models and to reduce uncertainty. The set-based similarity scores, driven by algorithmic randomness and Kolmogorov complexity, employ strangeness / typicality and p-values. We propose the application of the IIM framework to critical states prediction for complex physical systems;in particular, the prediction of cyclone genesis and intensification.

Intelligent Biometric Information Management

We advance here a novel methodology for robust intelligent biometric information management with inferences and predictions made using randomness and complexity concepts. Intelligence refers to learning, adap- tation, and functionality, and robustness refers to the ability to handle incomplete and/or corrupt adversarial information, on one side, and image and or device variability, on the other side. The proposed methodology is model-free and non-parametric. It draws support from discriminative methods using likelihood ratios to link at the conceptual level biometrics and forensics. It further links, at the modeling and implementation level, the Bayesian framework, statistical learning theory (SLT) using transduction and semi-supervised lea- rning, and Information Theory (IY) using mutual information. The key concepts supporting the proposed methodology are a) local estimation to facilitate learning and prediction using both labeled and unlabeled data;b) similarity metrics using regularity of patterns, randomness deficiency, and Kolmogorov complexity (similar to MDL) using strangeness/typicality and ranking p-values;and c) the Cover – Hart theorem on the asymptotical performance of k-nearest neighbors approaching the optimal Bayes error. Several topics on biometric inference and prediction related to 1) multi-level and multi-layer data fusion including quality and multi-modal biometrics;2) score normalization and revision theory;3) face selection and tracking;and 4) identity management, are described here using an integrated approach that includes transduction and boosting for ranking and sequential fusion/aggregation, respectively, on one side, and active learning and change/ outlier/intrusion detection realized using information gain and martingale, respectively, on the other side. The methodology proposed can be mapped to additional types of information beyond biometrics.

多个正态总体均值相等性检验方法的模拟比较

针对t个正态总体,提出均值相等性似然比检验.总结了三种检验方法,即似然比检验、bootstrap p-value检验和bootstrap检验.用Monte Carlo方法检验多个正态总体均值相等性问题,通过给出的模拟结果,比较了检验方法的有效性.

NIST随机性检测方法及应用

序列的随机性检测是密码学研究的一个重要课题,首先介绍了美国NIST测试标准,然后利用Linux系统下的makefile和sts软件两种方法对流密码ZUC生成的序列了进行随机性检测,16种测试结果表明ZUC的密钥流序列是随机的。

Asymptotic Inference for the Weak Stationary Double AR(1) Model

An AR(1) model with ARCH(1) error structure is known as the first-order double autoregressive (DAR(1)) model. In this paper, a conditional likelihood based method is proposed to obtain inference for the two scalar parameters of interest of the DAR(1) model. Theoretically, the proposed method has rate of convergence O(n-3/2). Applying the proposed method to a real-life data set shows that the results obtained by the proposed method can be quite different from the results obtained by the existing methods. Results from Monte Carlo simulation studies illustrate the supreme accuracy of the proposed method even when the sample size is small.

Epidemiological Analysis of the Coronavirus Disease Outbreak with Random Effects

Today,coronavirus appears as a serious challenge to the whole world.Epidemiological data of coronavirus is collected through media and web sources for the purpose of analysis.New data on COVID-19 are available daily,yet information about the biological aspects of SARS-CoV-2 and epidemiological characteristics of COVID-19 remains limited,and uncertainty remains around nearly all its parameters’values.This research provides the scientic and public health communities better resources,knowledge,and tools to improve their ability to control the infectious diseases.Using the publicly available data on the ongoing pandemic,the present study investigates the incubation period and other time intervals that govern the epidemiological dynamics of the COVID-19 infections.Formulation of the testing hypotheses for different countries with a 95%level of condence,and descriptive statistics have been calculated to analyze in which region will COVID-19 fall according to the tested hypothesized mean of different countries.The results will be helpful in decision making as well as in further mathematical analysis and control strategy.Statistical tools are used to investigate this pandemic,which will be useful for further research.The testing of the hypothesis is done for the differences in various effects including standard errors.Changes in states’variables are observed over time.The rapid outbreak of coronavirus can be stopped by reducing its transmission.Susceptible should maintain safe distance and follow precautionary measures regarding COVID-19 transmission.

随机性检测综述

随机性序列广泛应用于计算机科学的各个方面，特别是在密码学领域发挥了核心作用，保护了信息安全。实际应用中随机序列由伪随机数发生器产生，而随机性检测正是用于检测序列是否具有规则性。对现有随机性检测的研究成果进行综述，从随机性检测的多层次判别方法、随机性检测的相关性、随机性检测算法效率的优化等方面对研究成果进行梳理，并对现有随机性检测的不足以及今后的研究方向进行分析。

INSTANTANEOUS AVAILABILITY ASSESSMENT OF RENEWABLE COMPONENT IN EXPONENTIAL DISTRIBUTIONS

A renewable component with exponential failure and repair times is considered, and its instantaneous availability at time t is denoted by A（t）. This paper proposes two methods for constructing lower confidence limits of A（t） with Chebyshev inequation and generalized p-value approach.

Data Mining for Flooding Episode in the States of Alagoas and Pernambuco—Brazil

The increasing volume of data in the area of environmental sciences needs analysis and interpretation. Among the challenges generated by this “data deluge”, the development of efficient strategies for the knowledge discovery is an important issue. Here, statistical and tools from computational intelligence are applied to analyze large data sets from meteorology and climate sciences. Our approach allows a geographical mapping of the statistical property to be easily interpreted by meteorologists. Our data analysis comprises two main steps of knowledge extraction, applied successively in order to reduce the complexity from the original data set. The goal is to identify a much smaller subset of climatic variables that might still be able to describe or even predict the probability of occurrence of an extreme event. The first step applies a class comparison technique: p-value estimation. The second step consists of a decision tree (DT) configured from the data available and the p-value analysis. The DT is used as a predictive model, identifying the most statistically significant climate variables of the precipitation intensity. The methodology is employed to the study the climatic causes of an extreme precipitation events occurred in Alagoas and Pernambuco States (Brazil) at June/2010.

A Kullback-Leibler Divergence for Bayesian Model Diagnostics

This paper considers a Kullback-Leibler distance (KLD) which is asymptotically equivalent to the KLD by Goutis and Robert [1] when the reference model (in comparison to a competing fitted model) is correctly specified and that certain regularity conditions hold true (ref. Akaike [2]). We derive the asymptotic property of this Goutis-Robert-Akaike KLD under certain regularity conditions. We also examine the impact of this asymptotic property when the regularity conditions are partially satisfied. Furthermore, the connection between the Goutis-Robert-Akaike KLD and a weighted posterior predictive p-value (WPPP) is established. Finally, both the Goutis-Robert-Akaike KLD and WPPP are applied to compare models using various simulated examples as well as two cohort studies of diabetes.

Comparison of Outlier Techniques Based on Simulated Data

This research work employed a simulation study to evaluate six outlier techniques: t-Statistic, Modified Z-Statistic, Cancer Outlier Profile Analysis (COPA), Outlier Sum-Statistic (OS), Outlier Robust t-Statistic (ORT), and the Truncated Outlier Robust t-Statistic (TORT) with the aim of determining the technique that has a higher power of detecting and handling outliers in terms of their P-values, true positives, false positives, False Discovery Rate (FDR) and their corresponding Receiver Operating Characteristic (ROC) curves. From the result of the analysis, it was revealed that OS was the best technique followed by COPA, t, ORT, TORT and Z respectively in terms of their P-values. The result of the False Discovery Rate (FDR) shows that OS is the best technique followed by COPA, t, ORT, TORT and Z. In terms of their ROC curves, t-Statistic and OS have the largest Area under the ROC Curve (AUC) which indicates better sensitivity and specificity and is more significant followed by COPA and ORT with the equal significant AUC while Z and TORT have the least AUC which is not significant.

Comparison between Distractor Application on Both Radial &Ulnar Side and Radial Side Only for Fracture Distal Radius with Ulnar Styloid Fracture

Background: Fracture of distal radius with involvement of the ulnar styloid process is a common clinical problem. It can be treated conservatively, usually involving wrist immobilization in plaster cast or surgically. A key method of surgical fixation is external fixation by distractor. Distractor can be applied either only on the radial side or on both ulnar and radial sides. Materials and Methods: A prospective randomized and comparative study of 1 year duration was conducted on 32 patients admitted in the Department of Orthopaedics of BSMC & H in the age group of 20 to 75 years old with AO types B and C distal radius fracture along with involvement of the ulnar styloid process. The parameters studied were restoration of radial length, restoration of radial angle, intracarpal step-off and palmar tilt which were statistically evaluated and Fisher’s exact test was performed. The two tailed P-value was calculated and both the groups were statistically compared. Results: In our study, 37.5% patients in Group A and 81.25% in Group B had a radial difference Table 1, Chart 1). 43.75% patients in Group A and 87.5% in Group B had radial angle Table 2, Chart 2). 31.25% in Group A and 75% had intra carpal step off Table 3, Chart 3). 62.5% had an abnormal palmar tilt in Group A while only 6.25% had an abnormal palmar tilt in Group B which is extremely statistically significant. On an average, 2 mm of distraction was required in 75% patients of Group A while only 30% patients in Group B required distraction (Table 4, Chart 4). Conclusion: In our study, the radial difference, radial angle, intra carpal step off and palmar tilt returned significantly to normal in the patients treated with distractor on radial side only when compared with distractor application on both radial and ulnar sides for distal radius fracture with ulnar styloid process involvement. Also post-operative distraction required under image intensifier was higher in the group treated with distractor on either side than those with distractor only on radial side.

Application of Omori’s Decay Law to the 2001 Bhuj Aftershock Sequence for Kachchh Region of Western India

In the present study, the temporal behavior of 2001 Bhuj aftershock sequence in Kachchh region of western peninsular India is studied by the modified Omori law. The Omori law parameters p, c and K are determined with the standard errors by the maximum likelihood estimates using ZMAP algorithm in MatLab environment. The entire aftershock sequence is analyzed by diving it into three separate series with respect to time to weigh up the bigger earthquake of magnitude M 5.7 occurring on March 7, 2006 at Gedi fault. This study helps to understand the cumulative effect of the aftershocks generated by this bigger earthquake of the mainshock sequence. The results of this analysis are discussed with other studies of the different earthquake sequence for the different parts of the world and suggest that all the three series of Bhuj aftershock sequence follow the Omori relation. Values of parameter p vary significantly from series 1 to series 3, i.e., p-value varies significantly with time. Similarly, other two Omori law parameters K and c are also found to change significantly with time. These parameters are useful to describe temporal behavior of aftershocks and to forecast aftershock activity in time domain. Aftershock decay rate provides insight into stress release processes after the mainshock, thus helping to understand the heterogeneity of the fault zone properties and evaluate time-dependent seismic hazard analysis over the region.

A fiducial argument for generalized p-value

This paper provides a general method for constructing generalized p-value via the fiducial inference.Furthermore,the power properties of the generalized test are discussed.As illustrations, the two-parameter exponential distribution and unbalanced two-fold nested design are researched.It is shown that the resulting generalized p-values are of good frequency property.