Estimation of Return Level for Maximum Daily and Hourly Precipitation in Nagano Prefecture, Japan, Using the Extreme Value Theory

The weather in Nagano Prefecture, Japan, can be roughly classified into four types according to principal component analysis and k-means clustering. We predicted the extreme values of the maximum daily and hourly precipitation in Nagano Prefecture using the extreme value theory. For the maximum daily precipitation, the vales of ξ in Matsumoto, Karuizawa, Sugadaira, and Saku were positive;therefore, it has no upper bound and tends to take large values. Therefore, it is dangerous and caution is required. The values of ξ in Nagano, Kisofukushima, and Minamishinano were determined to be zero, therefore, there was no upper limit, the probability of obtaining a large value was low, and caution was required. We predicted the maximum return levels for return periods of 10, 20, 50, and 100 years along with respective 95% confidence intervals in Nagano, Matsumoto, Karuizawa, Sugadaira, Saku, Kisofukushima, and Minamishinano. In Matsumoto, the 100-year return level was 182 mm, with a 95% CI [129, 236]. In Minamishinano, the 100-year return level was 285 mm, with a 95% CI [173, 398]. The 100-year return levels for the maximum daily rainfall were 285, 271, and 271 mm in Minamishinano, Saku, and Karuizawa, respectively, where the changes in the daily maximum rainfall were larger than those at other points. Because these values are large, caution is required during heavy rainfall. The 100-year return levels for the maximum daily and hourly precipitation were similar in Karuizawa and Saku. In Sugadaira, the 100-year return level for a maximum hourly rainfall of 107.2 mm was larger than the maximum daily rainfall. Hence, it is necessary to be careful about short-term rainfall events.

Prognostic Value of Semi-Quantitative 18F-FDG PET/CT Parameters in Hodgkin’s Lymphoma

Objective:To assess the prognostic value of maximum standardized uptake value(SUVmax),metabolic tumor volume(MTV),and total lesion glycolysis(TLG)determined by 18F-fluorodeoxyglucose positron emission tomography-computed tomography(18F-FDG PET/CT)imaging in Hodgkin’s lymphoma patients.Methods:A total of 148 Hodgkin’s lymphoma patients diagnosed with lymph node biopsy from October 2014 to October 2015 were retrospectively analyzed followed by categorizing into good(125 cases)and poor(23 cases)prognosis groups.The chi-squared test was used to analyze the clinicopathological characteristics of Hodgkin’s lymphoma patients with the semi-quantitative 18F-FDG PET/CT parameters;the Spearman method was used to analyze the correlation between the semi-quantitative parameters and clinicopathological features of Hodgkin’s lymphoma;receiver operating characteristic curve was used to analyze the predictive value of the semi-quantitative parameters for poor prognosis of Hodgkin’s lymphoma patients.Results:Mean SUVmax,MTV,and TLG of the 148 cases of Hodgkin’s lymphoma were 7.26±2.38,12.46±3.14 cm3,and 76.83±18.56 g,respectively.Significant variations in the Ann Arbor stage and clinical classification were observed with different levels of semi-quantitative parameters(P<0.05).The semi-quantitative parameters were not correlated with age and gender(P>0.05)but positively correlated with Ann Arbor stage and clinical classification(P<0.05).These parameters in the poor prognosis group were higher than those in the good prognosis group(P<0.05).The area under the curve(AUC)of SUVmax,MTV,and TLG in predicting the poor prognosis group was 0.881,0.875,and 0.838,with cut-off values of 7.264,12.898 cm3,and 74.580g,as well as specificity of 88.8%,84.0%,and 78.4%,and sensitivity of 87.0%,87.0%,and 78.3%,respectively;the AUC of the combined prediction was 0.986,with a specificity of 97.6%and sensitivity of 86.3%.Conclusion:The semi-quantitative 18F-FDG PET/CT parameters provide valuable insights for Hodgkin’s lymphoma prognosis assessment.

Gradient Estimate of Solutions to a Class of Mean Curvature Equations with Prescribed Contact Angle Boundary Problem

This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained.

A New Method to Determine the Maximum Value of the Track Length of Alpha Particle in CR-39 Detector

The aim of this paper is to determine the maximum values of the track length (Lmax) of alpha particles in Nuclear Track Detector (type CR-39) using a new method by taking the relation between the etching time and the diameter square of alpha particle with different energies at constant bulk etch rate VB (1.45 μm/hr) by using TRACK_TEST program from Brun et al. function and Yu et al. function. Using the new equation, the maximum values of the track lengths of alpha particles measured in CR-39 detector have been found to be in a good agreement with the values measured by using Brun et al. function and Yu et al. function in TRACK_TEST program.

A circular zone counting method of identifying a Duffing oscillator state transition and determining the critical value in weak signal detection

Identifying state transition and determining the critical value of the Duffing oscillator are crucial to indicating external signal existence and have a great influence on detection accuracy in weak signal detection. A circular zone counting （CZC） method is proposed in this paper, by combining the Duffing oscillator＇s phase trajectory feature and numerical calculation for quickly and accurately identifying state transition and determining the critical value, to realize a high- efficiency weak signal detection. Detailed model analysis and method construction of the CZC method are introduced. Numerical experiments into the reliability of the proposed CZC method compared with the maximum Lyapunov exponent （MLE） method are carried out. The CZC method is demonstrated to have better detecting ability than the MLE method, and furthermore it is simpler and clearer in calculation to extend to engineering application.

Distributional expansion of maximum from logarithmic general error distribution

Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general error distribution is derived.

Estimation of Poisson-Generalized Pareto Compound Extreme Value Distribution by Probability-Weighted Moments and Empirical Analysis

This paper puts forward a Poisson-generalized Pareto (Poisson-GP) distribution. This new form of compound extreme value distribution expands the existing application of compound extreme value distribution, and can be applied to predicting financial risk, large insurance settlement and high-grade earthquake, etc. Compared with the maximum likelihood estimation (MLE) and compound moment estimation (CME), probability-weighted moment estimation (PWME) is used to estimate the parameters of the distribution function. The specific formulas are presented. Through Monte Carlo simulation with sample sizes 10, 20, 50, 100, 1 000, it is concluded that PWME is an efficient method and it behaves steadily. The mean square errors (MSE) of estimators by PWME are much smaller than those of estimators by CME, and there is no significant difference between PWME and MLE. Finally, an example of foreign exchange rate is given. For Dollar/Pound exchange rates from 1990-01-02 to 2006-12-29, this paper formulates the distribution function of the largest loss among the investment losses exceeding a certain threshold by Poisson-GP compound extreme value distribution, and obtains predictive values at different confidence levels.

Extreme value distributions of mixing two sequences with different MDA＇s

Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme value distribution ,n GZ(x) of this particular triangular array of the i.i.d. random variables Z1, , Z2, ,…, Zn n n ,nis discussed. We found a new form of the extreme value distribution ΛA(ρx)Λ(x)(0<ρ <1), which is not max-stable. It occurs if FX(x) and FY(x) belong to the same MDA(Λ). GZ(x) does not exist as mixture forms of the different types of extreme value distributions.

Importance of Generalized Logistic Distribution in Extreme Value Modeling

We consider a problem from stock market modeling, precisely, choice of adequate distribution of modeling extremal behavior of stock market data. Generalized extreme value (GEV) distribution and generalized Pareto (GP) distribution are the classical distributions for this problem. However, from 2004, [1] and many other researchers have been empirically showing that generalized logistic (GL) distribution is a better model than GEV and GP distributions in modeling extreme movement of stock market data. In this paper, we show that these results are not accidental. We prove the theoretical importance of GL distribution in extreme value modeling. For proving this, we introduce a general multivariate limit theorem and deduce some important multivariate theorems in probability as special cases. By using the theorem, we derive a limit theorem in extreme value theory, where GL distribution plays central role instead of GEV distribution. The proof of this result is parallel to the proof of classical extremal types theorem, in the sense that, it possess important characteristic in classical extreme value theory, for e.g. distributional property, stability, convergence and multivariate extension etc.

Optimal Threshold Determination for the Maximum Product of Spacing Methodology with Ties for Extreme Events

Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks down when there is a tie in the exceedances. This study offers a solution to model data even if it contains ties. To do so, an optimal threshold that gives more optimal parameters for extreme events, was determined. The study achieved its main objective by deriving a method that improved MPS method for determining an optimal threshold for extreme values in a data set containing ties, estimated the Generalized Pareto Distribution (GPD) parameters for the optimal threshold derived and compared these GPD parameters with GPD parameters determined through the standard MPS model. The study improved maximum product of spacing method and used Generalized Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of identifying extreme values. This study will help the statisticians in different sectors of our economy to model extreme events involving ties. To statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of the extreme event.

Extreme value distributions of mixing two sequences with the same MDA

Suppose {Xi, i 1} and {Yi, i 1} are two independent sequences with distribution functions ()XFx and ()YFx, respectively. Zi,n is the combination of Xi and Yi with a probability np for each i with 1 in. The extreme value distribution GZ(x) of this particular triangular array of the i.i.d. random variables Z1,n, Z2,n, ,L Zn,n is discussed. We found a new form of the extreme value distributions i) 12()()AxxaaFF and ii) 12()()AxxaaYY (a1<a2), which are not max-stable. It occurs if FX and FY belong to the same MDA(? or MDA(?.

Empirical Analysis of Value-at-Risk Estimation Methods Using Extreme Value Theory

This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and maximum likelihood estimation (MLE), according to their theoretical bases and computation procedures. Then, the estimation results are analyzed together with those of normal method and empirical method. The empirical research of foreign exchange data shows that the EVT methods have good characters in estimating VaR under extreme conditions and 'two-step subsample bootstrap' method is preferable to MLE.

A class of not max-stable extreme value distributions

The sequences {Zi , 1≤i≤n}, n≥1 have multi-nomial distribution among i.i.d. random variables {X1, , i≥1}, {X2, , ,n i i i≥1}, …, {Xm , i≥1}. The extreme value distribution GZ(x) of this particular triangular array of i.i.d. random variables Z1, , Z2, , …, ,i n n r ?1 Zn is discussed in this paper. We found a new type of not max-stable extreme value distributions, i) GZ (x) = ,n ∏Φα Ai(x)×Φαr (x); i i=1 r ?1 r?1 ii) GZ (x) = ∏Ψα Ai(x)×Ψαr (x); iii) GZ (x) = ∏Λ Ai(λix)×Λ(x), r≥2, 0<α1≤α2≤…≤αr and λi∈(0,1] for i, 1≤i≤r?1 which occur if i i=1 i=1 Fj, …, Fm belong to the same MDA.

Optimal Threshold Determination for Securities Exchange Volumes Using Improved Maximum Product of Spacing Methodology

To Statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of extreme event. Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks down when there is a tie in the exceedances. This study offers a solution to model data even when it contains ties. In the study, a method that improved MPS method for determining an optimal threshold for extreme values in a data set containing ties was derived. The Generalized Pareto Distribution (GPD) parameters for the optimal threshold were derived and compared to GPD parameters determined through the standard MPS model. The study improved the standard MPS methodology by introducing the concept of frequency and used Generalized Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of identifying extreme values. The improved MPS models and the standard models were applied to Nairobi Securities Exchange (NSE) trading volume data to determine the GPD parameters for different sectors registered in NSE market and their performance compared. It was realized that the improved MPS model performed better than the standard models. This study will help the Statisticians in different sectors of our economy to model extreme events involving ties.

The Dual of the Maximum Likelihood

The Maximum Likelihood method estimates the parameter values of a statistical model that maximizes the corresponding likelihood function, given the sample information. This is the primal approach that, in this paper, is presented as a mathematical programming specification whose solution requires the formulation of a Lagrange problem. A result of this setup is that the Lagrange multipliers associated with the linear statistical model (where sample observations are regarded as a set of constraints) are equal to the vector of residuals scaled by the variance of those residuals. The novel contribution of this paper consists in deriving the dual model of the Maximum Likelihood method under normality assumptions. This model minimizes a function of the variance of the error terms subject to orthogonality conditions between the model residuals and the space of explanatory variables. An intuitive interpretation of the dual problem appeals to basic elements of information theory and an economic interpretation of Lagrange multipliers to establish that the dual maximizes the net value of the sample information. This paper presents the dual ML model for a single regression and provides a numerical example of how to obtain maximum likelihood estimates of the parameters of a linear statistical model using the dual specification.

Application of Extreme Value Theory to Generation and Analysis of Pseudorandom Samples

The article deals with the methodology of pseudorandom data analysis. As a mathematical tool for carrying out the research the extreme value theory was used that creates one of the directions in mathematical statistics, and is related to investigating the extreme deviations from the median values in probability distributions. Also, the methods for estimating unknown parameters and algorithm of random-number generation are discussed. The models of treatment the extreme values are constructed which are based on machine generated sample and approach is proposed for their future application for constructing forecasting models.

降阶单元的新进展:内置了最大模误差估计器的自适应有限元法初探

该文基于初值问题中降阶单元的成功实践,进一步对一般边值问题提出无需超收敛计算、无需结构化网格、无需结点位移修正的降阶单元;进而提出以降阶单元作为最终解,且内置了最大模误差估计器的自适应有限元算法。该文对这一研究进展做简要介绍,并给出一维和二维边值问题的初步算例,以展示本法的可行性、有效性和可靠性。

公路隧道爆破振动对洞口区域建筑物的影响研究

在贵州省高速公路某隧道进行爆破开挖时,采用现场监测的方法研究隧道爆破振动对洞口区域建筑物的影响。依据测点布设原则,选取爆破振动影响区域具有代表性的4栋区域建筑物开展监测,根据第一次监测结果,结合现场的实际情况,确定区域建筑物的爆破振动安全允许标准为2.0 cm/s,以此推算爆破作业最大段装药量的限定范围为12.3~13.2 kg,据此将最大段装药量调整为13.0 kg。调整爆破方案后的监测结果表明:4个测点的峰值振速均小于2.0 cm/s,结合调整爆破方案前和调整爆破方案后的现场调研情况,验证选定的区域建筑物振动控制标准和最大段装药量取值的建议是合理可行的。

^(18)F-FDG PET/CT显像和血清学指标对前列腺肿瘤的诊断价值

目的 研究^(18)F-氟代脱氧葡萄糖(^(18)F-fluorodexyglucose,^(18)F-FDG)PET/CT显像和前列腺血清学指标诊断前列腺肿瘤的价值。方法 回顾性分析2013年8月至2021年12月在浙江大学医学院附属第二医院经病理证实的95例疑似前列腺肿瘤患者的^(18)F-FDG PET/CT图像与前列腺血清学指标。根据病理检查结果分为恶性组(n=77)和良性组(n=18)。采用受试者工作特征(receiver operating characteristic,ROC)曲线分析前列腺病灶的最大标准摄取值(maximum standardized uptake value,SUV_(max))与血清总前列腺特异性抗原(total prostate specific antigen,tPSA)、游离前列腺特异性抗原(free prostate specific antigen,fPSA)及游离/总前列腺特异性抗原比值(free/total prostate specific antigen,f/t-PSA)诊断前列腺良恶性病灶的最佳截断界值。结果 ROC曲线显示,SUV_(max)、tPSA、fPSA和f/t-PSA诊断前列腺良恶性病灶的最佳截断值分别为4.47、46.67 ng/mL、11.11 ng/mL和0.10。SUV_(max)、tPSA、fPSA和f/t-PSA的ROC曲线下面积(area under the curve,AUC)分别为0.658、0.897、0.842和0.836。^(18)F-FDG PET/CT显像、tPSA、f PSA和f/t-PSA对前列腺肿瘤的诊断敏感度分别是81.8%、97.4%、92.2%和83.1%,特异度分别是61.1%、27.8%、50.0%和50.0%,准确度分别是77.9%、84.2%、84.2%和76.8%。恶性组SUV_(max)、tPSA和fPSA均高于良性组,f/t-PSA低于良性组(均P<0.05)。^(18)F-FDG PET/CT检查显示,72例有远处转移病灶。结论 SUV_(max)、tPSA、fPSA和f/t-PSA均能鉴别前列腺良恶性病灶。^(18)F-FDG PET/CT显像在探测远处病灶方面更具有优势,能够为临床决策提供更好的帮助。

内置了最大模误差估计器的自适应有限元法——研究进展与展望

新近提出的降阶单元,将常规单元解答的最高次项视为误差项,当作内置的最大模误差估计器;将降低一次的解作为有限元最终解,从而一举实现了按最大模控制误差的自适应有限元算法。降阶单元最初针对结构时程分析的自适应步长算法提出,同时将其推广到一般的一维初值问题和边值问题。其后,将其推广到二维边值问题,构造了任意四边形和三角形降阶单元,已成功求解弹性薄膜挠度、弹性力学平面问题、平面和反平面裂纹问题、中厚板弯曲问题等各类二维问题。近期,又进一步将其推广到诸如非线性初值问题、薄膜结构找形问题、最小曲面问题、薄膜与地基接触、弹塑性扭转问题等非线性问题。该文对这一系列研究进展做了综述性介绍和展望,并给出各类问题的代表性数值算例以展示本法的有效性、灵活性、通用性和可靠性。