Let G be a simple connected graph with vertex set V(G)and edge set E(G).Then the Sombor index of graph G is defined as SO(G)=Σ_(uv∈E(G))√d^(2)(u)+d^(2)(v),where d(u)denotes the degree of vertex u.In this paper,the ...Let G be a simple connected graph with vertex set V(G)and edge set E(G).Then the Sombor index of graph G is defined as SO(G)=Σ_(uv∈E(G))√d^(2)(u)+d^(2)(v),where d(u)denotes the degree of vertex u.In this paper,the maximum and minimum values of the Sombor index for Halin graphs are obtained,and the corresponding extremal graphs are characterized.展开更多
Topological indices are a class of numerical invariants that can be used to predict the physicochemical properties of compounds and are widely used in quantum chemistry,molecular biology and other research field.For a...Topological indices are a class of numerical invariants that can be used to predict the physicochemical properties of compounds and are widely used in quantum chemistry,molecular biology and other research field.For a(molecular)graph G with vertex set V(G)and edge set E(G),the Sombor index is defined as SO(G)=∑_(uv∈E(G))√d^(2)_(G)(u)+d^(2)_(G)(v),where d_(G)(u)denotes the degree of vertex u in G.Accordingly,the multiplicative Sombor index is defined asП_(SO)(G)=П_(uv∈E(G))√d^(2)_(G)(u)+d^(2)_(G)(v).A molecular tree is a tree with maximum degree∆≤4.In this paper,we first determine the maximum molecular trees with respect to multiplicative Sombor index.Then we determine the first thirteen minimum(molecular)trees with respect to multiplicative Sombor index.展开更多
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, whe...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.展开更多
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 proba...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.展开更多
In using the PGCEVD （Poisson-Gumbel Compound Extreme Value Distribution） model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing...In using the PGCEVD （Poisson-Gumbel Compound Extreme Value Distribution） model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing the principle of the threshold selection of PGCEVD model and in combination of the change point statistical methods, this paper proposes a new method for quantitative calculation of the threshold in PGCEVD model. Eleven samples from five engineering points in several coastal waters of Guangdong and Hainan, China, are calculated and analyzed by using PGCEVD model and the traditional Pearson type III distribution （P-III） model, respectively. By comparing the results of the two models, it is shown that the new method of selecting the optimal threshold is feasible. PGCEVD model has more stable results than that of P-III model and can be used for the return wave height in every direction.展开更多
The research of carbon content along the casting direction of 82B cord steel billets is of great significance for improvingthe quality of cord products from subsequent processing.However,the traditional segregation an...The research of carbon content along the casting direction of 82B cord steel billets is of great significance for improvingthe quality of cord products from subsequent processing.However,the traditional segregation and billets quality evaluationmethods have certain limitations,such as sampling length and analysis area.which affect the accuracy of quality judgment.Thus.the statistics of extreme values(SEV)was introduced to predict the maximum value of carbon element contentalong the casting direction,which can quantitatively characterize the segregation degree.The size of the selected billet is150 mm×150 mm,and the sampling location is the centerline of the billet.The experiment was conducted by consideringthe effect of cooling intensity and casting speed on the maximum value of carbon element content.Firstly,the calculationresults show that the SEN method can predict the maximum value of carbon element content along the casting directionof 82B cord steel,and the SEV method is proved to be effective by analyzing the carbon distribution and fluctuation in billets.To some extent,the SEV method can break the limitations of the sampling length and analysis area by predicting themaximum value of carbon element on a larger range of continuous casting billets with few samples.During the continuouscasting process the increase in cooling intensity makes the surface shrinking rate increase,which can slow down the flowof solute-enriched liquid to the center,and the center segregation can be reduced.On the other hand,the function area ofthe final electromagnetic stirring can be expanded with the increase in the casting speed,which can reduce the concentration of carbon element in the center of the billets and reduce the maximum value of carbon element content.Ilt can providea new theoretical reference for the quantitative calculation of carbon content in continuous casting billets and the qualityevaluation of continuous casting billcts.展开更多
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 ...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.展开更多
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 ...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.展开更多
GARCH-M ( generalized autoregressive conditional heteroskedasticity in the mean) model is used to analyse the volatility clustering phenomenon in mobile communication network traffic. Normal distribution, t distributi...GARCH-M ( generalized autoregressive conditional heteroskedasticity in the mean) model is used to analyse the volatility clustering phenomenon in mobile communication network traffic. Normal distribution, t distribution and generalized Pareto distribution assumptions are adopted re- spectively to simulate the random component in the model. The demonstration of the quantile of network traffic series indicates that common GARCH-M model can partially deal with the "fat tail" problem. However, the "fat tail" characteristic of the random component directly affects the accura- cy of the calculation. Even t distribution is based on the assumption for all the data. On the other hand, extreme value theory, which only concentrates on the tail distribution, can provide more ac- curate result for high quantiles. The best result is obtained based on the generalized Pareto distribu- tion assumption for the random component in the GARCH-M model.展开更多
A statistic method, statistics of extreme values （SEV）, was described in detail, which can esti mate the size of maximum inclusion in steel. The characteristic size of the maximum inclusion in a high clean bearing s...A statistic method, statistics of extreme values （SEV）, was described in detail, which can esti mate the size of maximum inclusion in steel. The characteristic size of the maximum inclusion in a high clean bearing steel （GCrl5） was evaluated by this method, and the morphology and corn position of large inclusions found were analyzed by scanning electron microscopy （SEM）. When standard inspection area （S0） is 280 mm2, the characteristic size of the biggest inclusion found in 30 standard inspection area is 23.93 μm, and it has a 99.9% probability of the characteristic size of maximum inclusion predicted being no larger than 36.85μm in the experimental steel. SEM result shows that large inclusions found are mainly composed of CaS, calcium-aluminate and MgO. Compositing widely exists in large inclusions in high clean bearing steel. Compared with traditional evaluation method, SEV method mainly focuses on inclusion size, and the esti- mation result is not affected by inclusion types. SEV method is suitable for the inclusion eval uation of high clean bearing steel.展开更多
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) distributi...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.展开更多
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 e...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, <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em>ξ</em></span></span> was evaluated as <span style="white-space:nowrap;"><span style="white-space:nowrap;">−</span></span>0.163, with a 95% confidence interval of [<span style="white-space:nowrap;"><span style="white-space:nowrap;">−</span></span>0.260, <span style="white-space:nowrap;"><span style="white-space:nowrap;">−</span></span>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.展开更多
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 m...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.展开更多
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 ar...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.展开更多
The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d, random variables {X1,i, i≥1}, {X2,i, i≥1 } {Xm,i, i≥1 }. The extreme value distribution Gz（x） of this particular triangular array of ...The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d, random variables {X1,i, i≥1}, {X2,i, i≥1 } {Xm,i, i≥1 }. The extreme value distribution Gz（x） of this particular triangular array of i.i,d, random variables Z1,n, Z2 n,...,Zn,n is discussed. A new type of not max-stable extreme value distributions which are Fréchet mixture, Gumbel mixture and Weibull mixture has been found if Fj,…… Fm belong to the same MDA. Whether mixtures of different types of extreme value distributions exist or not and the more general case are discussed in this paper. We found that Gz（x） does not exist as mixture forms of the different types of extreme value distributions after we investigated all cases.展开更多
This paper studies the dependence order among multivariate extreme value dis- tributions with a fixed marginal distribution. Making use of copulas to prove that the set organized by multivariate extreme value distribu...This paper studies the dependence order among multivariate extreme value dis- tributions with a fixed marginal distribution. Making use of copulas to prove that the set organized by multivariate extreme value distributions and the dependence order defined in it is a partial order set. Finally, the maximum and minimum values of the set is discussed.展开更多
It is very im portant to analyze network traffic in the network control and management. In thi s paper, extreme value theory is first introduced and a model with threshold met hods is proposed to analyze the character...It is very im portant to analyze network traffic in the network control and management. In thi s paper, extreme value theory is first introduced and a model with threshold met hods is proposed to analyze the characteristics of network traffic. In this mode l, only some traffic data that is greater than threshold value is considered. Th en the proposed model with the trace is simulated by using S Plus software. The modeling results show the network traffic model constructed from the extreme va lue theory fits well with that of empirical distribution. Finally, the extreme v alue model with the FARIMA(p,d,q) modeling is compared. The anal ytical results illustrate that extreme value theory has a good application foreg round in the statistic analysis of network traffic. In addition, since only some traffic data which is greater than the threshold is processed, the computation overhead is reduced greatly.展开更多
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 sta...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.展开更多
In recent years, the red tide erupted frequently, and caused a great economic loss. At present, most literatures emphasize the academic research on the growth mechanism of red tide alga. In order to find out the chara...In recent years, the red tide erupted frequently, and caused a great economic loss. At present, most literatures emphasize the academic research on the growth mechanism of red tide alga. In order to find out the characters of red tide in detail and improve the precision of forecast, this paper gives some new approaches to dealing with the red tide. By the extreme values, we deal with the red tide frequency analysis and get the estimation of T-times red tide level U (T), which is the level once the consistence of red tide alga exceeds on the average in a period of T times.展开更多
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 m...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.展开更多
基金supported by the National Natural Science Foundation of China(No.12201634)the Hunan Provincial Natural Science Foundation of China(Nos.2020JJ4423,2023JJ30070)。
文摘Let G be a simple connected graph with vertex set V(G)and edge set E(G).Then the Sombor index of graph G is defined as SO(G)=Σ_(uv∈E(G))√d^(2)(u)+d^(2)(v),where d(u)denotes the degree of vertex u.In this paper,the maximum and minimum values of the Sombor index for Halin graphs are obtained,and the corresponding extremal graphs are characterized.
基金Supported by the National Natural Science Foundation of China(Grant No.11971180)the Natural Science Foundation of Guangdong Provine(Grant No.2019A1515012052)+1 种基金the Characteristic Innovation Project of General Colleges and Universities in Guangdong Province(Grant No.2022KTSCX225)the Guangdong Education and Scientific Research Project(Grant No.2021GXJK159)。
文摘Topological indices are a class of numerical invariants that can be used to predict the physicochemical properties of compounds and are widely used in quantum chemistry,molecular biology and other research field.For a(molecular)graph G with vertex set V(G)and edge set E(G),the Sombor index is defined as SO(G)=∑_(uv∈E(G))√d^(2)_(G)(u)+d^(2)_(G)(v),where d_(G)(u)denotes the degree of vertex u in G.Accordingly,the multiplicative Sombor index is defined asП_(SO)(G)=П_(uv∈E(G))√d^(2)_(G)(u)+d^(2)_(G)(v).A molecular tree is a tree with maximum degree∆≤4.In this paper,we first determine the maximum molecular trees with respect to multiplicative Sombor index.Then we determine the first thirteen minimum(molecular)trees with respect to multiplicative Sombor index.
文摘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.
基金National Natural Science Foundation of China for Innovative Research Groups Under Grant No. 50321803 National Natural Science Foundation of China for Young Scholars Under Grant No. 10402030
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.10902039)the Major Project Research of the Ministry of Railways of the People's Republic of China(Grant No.2010-201)
文摘In using the PGCEVD （Poisson-Gumbel Compound Extreme Value Distribution） model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing the principle of the threshold selection of PGCEVD model and in combination of the change point statistical methods, this paper proposes a new method for quantitative calculation of the threshold in PGCEVD model. Eleven samples from five engineering points in several coastal waters of Guangdong and Hainan, China, are calculated and analyzed by using PGCEVD model and the traditional Pearson type III distribution （P-III） model, respectively. By comparing the results of the two models, it is shown that the new method of selecting the optimal threshold is feasible. PGCEVD model has more stable results than that of P-III model and can be used for the return wave height in every direction.
基金The authors are very grateful for support from United Funds between National Natural Science Foundation and Baowu Steel Group Corporation Limited from China(No.U1860101)Chongqing Fundamental Research and Cutting-Edge Technology Funds(No.cstc2017jcyjAX0019).
文摘The research of carbon content along the casting direction of 82B cord steel billets is of great significance for improvingthe quality of cord products from subsequent processing.However,the traditional segregation and billets quality evaluationmethods have certain limitations,such as sampling length and analysis area.which affect the accuracy of quality judgment.Thus.the statistics of extreme values(SEV)was introduced to predict the maximum value of carbon element contentalong the casting direction,which can quantitatively characterize the segregation degree.The size of the selected billet is150 mm×150 mm,and the sampling location is the centerline of the billet.The experiment was conducted by consideringthe effect of cooling intensity and casting speed on the maximum value of carbon element content.Firstly,the calculationresults show that the SEN method can predict the maximum value of carbon element content along the casting directionof 82B cord steel,and the SEV method is proved to be effective by analyzing the carbon distribution and fluctuation in billets.To some extent,the SEV method can break the limitations of the sampling length and analysis area by predicting themaximum value of carbon element on a larger range of continuous casting billets with few samples.During the continuouscasting process the increase in cooling intensity makes the surface shrinking rate increase,which can slow down the flowof solute-enriched liquid to the center,and the center segregation can be reduced.On the other hand,the function area ofthe final electromagnetic stirring can be expanded with the increase in the casting speed,which can reduce the concentration of carbon element in the center of the billets and reduce the maximum value of carbon element content.Ilt can providea new theoretical reference for the quantitative calculation of carbon content in continuous casting billets and the qualityevaluation of continuous casting billcts.
基金National Natural Science Foundation of China (No.70573077)
文摘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.
文摘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.
基金Supported by University and College Doctoral Subject Special Scientific Research Fund( No. 20040056041).
文摘GARCH-M ( generalized autoregressive conditional heteroskedasticity in the mean) model is used to analyse the volatility clustering phenomenon in mobile communication network traffic. Normal distribution, t distribution and generalized Pareto distribution assumptions are adopted re- spectively to simulate the random component in the model. The demonstration of the quantile of network traffic series indicates that common GARCH-M model can partially deal with the "fat tail" problem. However, the "fat tail" characteristic of the random component directly affects the accura- cy of the calculation. Even t distribution is based on the assumption for all the data. On the other hand, extreme value theory, which only concentrates on the tail distribution, can provide more ac- curate result for high quantiles. The best result is obtained based on the generalized Pareto distribu- tion assumption for the random component in the GARCH-M model.
基金funded by National Natural Science Foundation of China(51474076)International S&T Cooperation Program(ISTCP)of China(2015DFG51950)
文摘A statistic method, statistics of extreme values （SEV）, was described in detail, which can esti mate the size of maximum inclusion in steel. The characteristic size of the maximum inclusion in a high clean bearing steel （GCrl5） was evaluated by this method, and the morphology and corn position of large inclusions found were analyzed by scanning electron microscopy （SEM）. When standard inspection area （S0） is 280 mm2, the characteristic size of the biggest inclusion found in 30 standard inspection area is 23.93 μm, and it has a 99.9% probability of the characteristic size of maximum inclusion predicted being no larger than 36.85μm in the experimental steel. SEM result shows that large inclusions found are mainly composed of CaS, calcium-aluminate and MgO. Compositing widely exists in large inclusions in high clean bearing steel. Compared with traditional evaluation method, SEV method mainly focuses on inclusion size, and the esti- mation result is not affected by inclusion types. SEV method is suitable for the inclusion eval uation of high clean bearing steel.
文摘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.
文摘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, <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em>ξ</em></span></span> was evaluated as <span style="white-space:nowrap;"><span style="white-space:nowrap;">−</span></span>0.163, with a 95% confidence interval of [<span style="white-space:nowrap;"><span style="white-space:nowrap;">−</span></span>0.260, <span style="white-space:nowrap;"><span style="white-space:nowrap;">−</span></span>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.
基金the National Natural Science Foundation of China (No. 79970041).
文摘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.
基金Project partially supported by the Swiss National Science Foundation
文摘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.
基金Project partially supported by the National Natural Science Foundation of Switzerland
文摘The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d, random variables {X1,i, i≥1}, {X2,i, i≥1 } {Xm,i, i≥1 }. The extreme value distribution Gz（x） of this particular triangular array of i.i,d, random variables Z1,n, Z2 n,...,Zn,n is discussed. A new type of not max-stable extreme value distributions which are Fréchet mixture, Gumbel mixture and Weibull mixture has been found if Fj,…… Fm belong to the same MDA. Whether mixtures of different types of extreme value distributions exist or not and the more general case are discussed in this paper. We found that Gz（x） does not exist as mixture forms of the different types of extreme value distributions after we investigated all cases.
文摘This paper studies the dependence order among multivariate extreme value dis- tributions with a fixed marginal distribution. Making use of copulas to prove that the set organized by multivariate extreme value distributions and the dependence order defined in it is a partial order set. Finally, the maximum and minimum values of the set is discussed.
文摘It is very im portant to analyze network traffic in the network control and management. In thi s paper, extreme value theory is first introduced and a model with threshold met hods is proposed to analyze the characteristics of network traffic. In this mode l, only some traffic data that is greater than threshold value is considered. Th en the proposed model with the trace is simulated by using S Plus software. The modeling results show the network traffic model constructed from the extreme va lue theory fits well with that of empirical distribution. Finally, the extreme v alue model with the FARIMA(p,d,q) modeling is compared. The anal ytical results illustrate that extreme value theory has a good application foreg round in the statistic analysis of network traffic. In addition, since only some traffic data which is greater than the threshold is processed, the computation overhead is reduced greatly.
文摘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.
基金This study is supported by the National Natural Science Foundation of China under No.10472077.
文摘In recent years, the red tide erupted frequently, and caused a great economic loss. At present, most literatures emphasize the academic research on the growth mechanism of red tide alga. In order to find out the characters of red tide in detail and improve the precision of forecast, this paper gives some new approaches to dealing with the red tide. By the extreme values, we deal with the red tide frequency analysis and get the estimation of T-times red tide level U (T), which is the level once the consistence of red tide alga exceeds on the average in a period of T times.
文摘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.
