Bivariate Analysis of Pollutants Monthly Maxima in Mexico City Using Extreme Value Distributions and Copula

In the present work, we are interested in studying the joint distributions of pairs of the monthly maxima of the pollutants used by the environmental authorities in Mexico City to classify the air quality in the metropolitan area. In order to obtain the joint distributions a copula will be considered. Since we are analyzing the monthly maxima, the extreme value distributions of Weibull and Fréchet are taken into account. Using these two distributions as marginal distributions in the copula a Bayesian inference was made in order to estimate the parameters of both distributions and also the association parameters appearing in the copula model. The pollutants taken into account are ozone, nitrogen dioxide, sulphur dioxide, carbon monoxide, and particulate matter with diameters smaller than 10 and 2.5 microns obtained from the Mexico City monitoring network. The estimation was performed by taking samples of the parameters generated through a Markov chain Monte Carlo algorithm implemented using the software OpenBugs. Once the algorithm is implemented it is applied to the pairs of pollutants where one of the coordinates of the pair is ozone and the other varies on the set of the remaining pollutants. Depending on the pollutant and the region where they were collected, different results were obtained. Hence, in some cases we have that the best model is that where we have a Fréchet distribution as the marginal distribution for the measurements of both pollutants and in others the most suitable model is the one assuming a Fréchet for ozone and a Weibull for the other pollutant. Results show that, in the present case, the estimated association parameter is a good representation to the correlation parameters between the pair of pollutants analyzed. Additionally, it is a straightforward task to obtain these correlation parameters from the corresponding association parameters.

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.

The Pickands' Estimator of the Negative Extreme-value Index

提出一类极值指数为负时的相似于Pickand’s型的新的极值指数估计量 。

Extreme value distribution and reliability of nonlinear stochastic structures

A new approach to evaluate the extreme value distribution （EVD） of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed probability density evolution method, which enables the instantaneous probability density functions of the stochastic responses to be captured. In the proposed method, a virtual stochastic process is first constructed to satisfy the condition that the extreme value of the response equals the value of the constructed process at a certain instant of time. The probability density evolution method is then applied to evaluate the instantaneous probability density function of the response, yielding the EVD. The reliability is therefore available through a simple integration over the safe domain. A numerical algorithm is developed using the Number Theoretical Method to select the discretized representative points. Further, a hyper-ball is imposed to sieve the points from the preceding point set in the hypercube. In the numerical examples, the EVD of random variables is evaluated and compared with the analytical solution. A frame structure is analyzed to capture the EVD of the response and the dynamic reliability. The investigations indicate that the proposed approach provides reasonable accuracy and efficiency.

Extreme value theory applied to the auroral electrojet indices

The study of extreme weather and space events has gained paramount importance in modern society owing to rapid advances in high technology.Understanding and describing exceptional occurrences plays a crucial role in making decisive assessments of their potential impact on technical,economic,and social aspects in various fields.This research focuses on analyzing the hourly values of the auroral electrojet(AE)geomagnetic index from 1957 to 2019 by using the peak over threshold method in extreme value theory.By fitting the generalized Pareto distribution to extreme AE values,shape parameter indices were derived,revealing negative values that establish an upper bound for this time series.Consequently,it became evident that the AE values had reached a plateau,suggesting that extreme events exceeding the established upper limit are rare.As a result,although the need for diligent precautions to mitigate the consequences of such extreme events persists,surpassing the upper limit of AE values becomes increasingly challenging.It is also possible to observe an aurora in the middle-and low-latitude regions during the maximum period of the AE index.

Optical design of the time-resolved ARPES beamline of the new material spectroscopy experimental station for the update of CAEP THz-FEL facility

The Chinese Academy of Engineering Physics Terahertz Free Electron Laser Facility(CAEP THz FEL,CTFEL)is the only high-average power free electron laser terahertz source based on superconducting accelerators in China.The update of the CTFEL is now undergoing and will expand the frequency range from 0.1–4.2 THz to 0.1–125 THz.Two experimental stations for material spectroscopy and biomedicine will be built.A high harmonic generation(HHG)lightsource based beamline at the material spectroscopy experimental station for time-resolved angle-resolved photoemission spectroscopy(ARPES)research will be constructed and the optical design is presented.The HHG lightsource covers the extreme ultraviolet(XUV)photon energy range of 20–50 eV.A Czerny–Turner monochromator with two plane gratings worked in conical diffraction configuration is employed to maintain the transmission efficiency and preserve the pulse time duration.The calculated beamline transmission efficiency is better than 5%in the whole photon energy range.To our knowledge,this is the first time in China to combine THz-infrared FEL with HHG light source,and this experimental station will be a powerful and effective instrument that will give new research opportunities in the future for users doing research on the dynamic evolution of the excited electron band structure of a material’s surface.

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.

Numerical Simulation and Analysis of Storm Surges Under Different Extreme Weather Event and Typhoon Experiments in the South Yellow Sea

In this study,a coupled tide-surge-wave model was developed and applied to the South Yellow Sea.The coupled model simulated the evolution of storm surges and waves caused by extreme weather events,such as tropical cyclones,cold waves,extratropical cyclones coupled with a cold wave,and tropical cyclones coupled with a cold wave.The modeled surge level and significant wave height matched the measured data well.Simulation results of the typhoon with different intensities revealed that the radius to the maximum wind speed of a typhoon with 1.5 times wind speed decreased,and its influence range was farther away from the Jiangsu coastal region;moreover,the impact on surge levels was weakened.Thereafter,eight hypothetical typhoons based on Typhoon Chan-hom were designed to investigate the effects of varying typhoon tracks on the extreme value and spatial distribution of storm surges in the offshore area of Jiangsu Province.The typhoon along path 2 mainly affected the Rudong coast,and the topography of the Rudong coast was conducive to the increase in surge level.Therefore,the typhoon along path 2 induced the largest surge level,which reached up to 2.91 m in the radial sand ridge area.The maximum surge levels in the Haizhou Bay area and the middle straight coastline area reached up to 2.37 and 2.08 m,respectively.In terms of typhoons active in offshore areas,the radial sand ridge area was most likely to be threatened by typhoon-induced storm surges.

Crop yields and soil organic carbon dynamics in a long-term fertilization experiment in an extremely arid region of northern Xinjiang, China

A long-term fertilization experiment was set up in northern Xinjiang, China to evaluate the dynamics of crop production and soil organic carbon （SOC） from 1990 to 2012 with seven fertilization treatments. The seven treatments included an unfertilized control （CK） and six different combinations of phosphorus （P）, potassium （K）, nitrogen （N）, straw （S） and animal manure （M）. The balanced fertilization treatments had significantly （P〈0.05） higher average yields than the unbalanced ones. The treatment with 2/3 N from potassium sulfate （NPK） and 1/3 N from farmyard manure （NPKM） had a higher average yield than the other treatments. The average yields （over the 23 years） in the treatments of NPK, and urea, calcium superphosphate （NP） did not differ significantly （P〉0.05） but were higher than that in the treatment with urea and potassium sulfate （NK; P〈0.05）. The results also show that the highest increases in SOC （P〈0.05） occurred in NPKM with a potential increase of 1.2 t C/（hm2.a）. The increase in SOC was only 0.31, 0.30 and 0.12 t C/（hm2.a） for NPKS （9/10 N from NPK and 1/10 N from straw）, NPK and NP, respectively; and the SOC in the NP, NK and CK treatments were approaching equilibrium and so did not rise or fall significantly over the 23-year experiment. A complete NPK plus manure fertilization program is recommended for this extremely arid region to maximize both yields and carbon sequestration.

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.

How Sense of Ritual in Tourism Impacts Tourists’Co-Creation of Tourism Experience Values:A Study Based on the Theory of Value Co-Creation

Establishing a sense of ritual within tourism consumption scenarios offers tourists the opportunity for interactive engagement.Drawing upon the value co-creation theory,this study constructed an influence mechanism model to examine tourists'active engagement in the process of co-creating tourism experience values.It employed Partial Least Squares Structural Equation Modeling(PLS-SEM)to empirically test the proposed hypotheses.The findings demonstrate that the model constructed in the present study exhibits robust reliability,validity,and explanatory power.The perception of the sense of ritual in tourism exerts a significant positive influence on tourists’co-creation of tourism experience values,thereby significantly enhancing both the communitas and flow experienced by tourists during their travels.Moreover,such communitas and flow can mediate the influence of the sense of ritual in tourism on tourists’co-creation of tourism experience values.This study contributes to advancing the current research on tourists’co-creation of tourism experience values and the sense of ritual in tourism,thereby providing theoretical foundations for cultivating a sense of ritual within tourism consumption scenarios.

Analysis of Japan and World Records in the 100 m Dash Using Extreme Value Theory

Extreme value theory provides methods to analyze the most extreme parts of data. We predicted the ultimate 100 m dash records for men and women for specific periods using the generalized extreme value (GEV) distribution. The various diagnostic plots, which assessed the accuracy of the GEV model, were well fitted to the 100 m records in the world and Japan, validating the model. The men’s world record had a shape parameter of -0.250 with a 95% confidence interval of [-0.391, -0.109]. The 100 m record had a finite limit and a calculated upper limit was 9.46 s. The return level estimates for the men’s world record were 9.74, 9.62, and 9.58 s with a 95% confidence interval of [9.69, 9.79], [9.54, 9.69], and [9.48, 9.67] for 10-, 100- and 350-year return periods, respectively. In one year, the probability of occurrence for a new world record of men, 9.58 s (Usain Bolt), was 1/350, while that for women, 10.49 s (Florence Griffith-Joyner), was about 1/100, confirming it was more difficult for men to break records than women.

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.

Clinical Value of Predictive Nursing Intervention on Deep Venous Thrombosis of Lower Extremities after Cesarean Section

[Objectives]To explore the clinical nursing value of predictive nursing intervention in patients with deep venous thrombosis of lower extremities after cesarean section.[Methods]From December 2022 to April 2023,105 pregnant and lying-in women who were hospitalized in the Gynecology Department of Pingquan Hospital and underwent cesarean section and met the inclusion criteria were included as the study objects.According to the medical records,they were divided into observation group(n=52 cases)and control group(n=53 cases).The clinical experimental subjects were divided into two groups.One group was the control group with routine nursing,and the other group was the observation group with predictive nursing intervention.The number of cases of deep venous thrombosis of lower extremities in the two groups was recorded to evaluate the clinical value.[Results]The incidence of deep venous thrombosis of lower extremities in the two groups after cesarean section was compared,and it was suggested that the incidence of the observation group was lower than that of the control group(P<0.05).[Conclusions]Special predictive nursing intervention can greatly reduce the incidence of deep venous thrombosis of lower extremities after cesarean section,improve nursing satisfaction,and improve clinical efficacy,which is worthy of recommendation.

Analyzing the Annual Maximum Magnitude of Earthquakes in Japan by Extreme Value Theory

One of the most important and interesting issues associated with the earthquakes is the long-term trend of the extreme events. Extreme value theory provides methods for analysis of the most extreme parts of data. We estimated the annual maximum magnitude of earthquakes in Japan by extreme value theory using earthquake data between 1900 and 2019. Generalized extreme value (GEV) distribution was applied to fit the extreme indices. The distribution was used to estimate the probability of extreme values in specified time periods. The various diagnostic plots for assessing the accuracy of the GEV model fitted to the magnitude of maximum earthquakes data in Japan gave the validity of the GEV model. The extreme value index, ξ was evaluated as −0.163, with a 95% confidence interval of [−0.260, −0.0174] by the use of profile likelihood. Hence, the annual maximum magnitude of earthquakes has a finite upper limit. We obtained the maximum return level for the return periods of 10, 20, 50, 100 and 500 years along with their respective 95% confidence interval. Further, to get a more accurate confidence interval, we estimated the profile log-likelihood. The return level estimate was obtained as 7.83, 8.60 and 8.99, with a 95% confidence interval of [7.67, 8.06], [8.32, 9.21] and [8.61, 10.0] for the 10-, 100- and 500-year return periods, respectively. Hence, the 2011 off the Pacific coast of Tohoku Earthquake, which was the largest in the observation history of Japan, had a magnitude of 9.0, and it was a phenomenon that occurs once every 500 year.

The Maximum and Minimum Value of Exponential RandićIndices of Quasi-Tree Graph

The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.

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.

Estimation of Dynamic VaR in Chinese Stock Markets Based on Time Scale and Extreme Value Theory

The accuracy and time scale invariance of value-at-risk （VaR） measurement methods for different stock indices and at different confidence levels are tested. Extreme value theory （EVT） is applied to model the extreme tail of standardized residual series of daily/weekly indices losses, and parametric and nonparametric methods are used to estimate parameters of the general Pareto distribution （GPD）, and dynamic VaR for indices of three stock markets in China. The accuracy and time scale invariance of risk measurement methods through back-testing approach are also examined. Results show that not all the indices accept time scale invariance; there are some differences in accuracy between different indices at various confidence levels. The most powerful dynamic VaR estimation methods are EVT-GJR-Hill at 97.5% level for weekly loss to Shanghai stock market, and EVT-GARCH-MLE （Hill） at 99.0% level for weekly loss to Taiwan and Hong Kong stock markets, respectively.

Limiting Distribution of Extreme Values for FGM Random Sequences

This paper mainly study extreme values of FGM random sequences.We prove a technique theorem by the dependence structure of FGM sequences,and further obtain the limiting distributions of maxima and k-th largest for stationary FGM random sequences.