How to choose an optimal threshold is a key problem in the generalized Pareto distribution (GPD) model. This paper attains the exact threshold by testing for GPD,and shows that GPD model allows the actuary to easily...How to choose an optimal threshold is a key problem in the generalized Pareto distribution (GPD) model. This paper attains the exact threshold by testing for GPD,and shows that GPD model allows the actuary to easily estimate high quantiles and the probable maximum loss from the medical insurance claims data.展开更多
The generalized Pareto distribution model is a kind of hydrocarbon pool size probability statistical method for resource assessment. By introducing the time variable, resource conversion rate and the geological variab...The generalized Pareto distribution model is a kind of hydrocarbon pool size probability statistical method for resource assessment. By introducing the time variable, resource conversion rate and the geological variable, resource density, such model can describe not only different types of basins, but also any exploration samples at different phases of exploration, up to the parent population. It is a dynamic distribution model with profound geological significance and wide applicability. Its basic principle and the process of resource assessment are described in this paper. The petroleum accumulation system is an appropriate assessment unit for such method. The hydrocarbon resource structure of the Huanghua Depression in Bohai Bay Basin was predicted by using this model. The prediction results accord with the knowledge of exploration in the Huanghua Depression, and point out the remaining resources potential and structure of different petroleum accumulation systems, which are of great significance for guiding future exploration in the Huanghua Depression.展开更多
The Pareto distribution plays an important role in various areas of research. In this paper, the average run length (ARL) unbiased control charts, which monitor the shape and threshold parameters of the Pareto distr...The Pareto distribution plays an important role in various areas of research. In this paper, the average run length (ARL) unbiased control charts, which monitor the shape and threshold parameters of the Pareto distribution respectively, are proposed when the incontrol parameters are known. The effects of parameter estimation on the performance of the proposed control charts are also studied. Results show that the control charts with the estimated parameters are not suitable to be used in the known parameter case, thus the ARL-unbiased control charts for the shape and threshold parameters with the desired ARLo, which consider the variability of the parameter estimates, are further developed. The performance of the proposed control charts is investigated in terms of the ARL. Finally, an example is given to illustrate the proposed control charts.展开更多
This paper proposes a new methodology to select an optimal threshold level to be used in the peak over threshold (POT) method for the prediction of short-term distributions of load extremes of offshore wind turbines...This paper proposes a new methodology to select an optimal threshold level to be used in the peak over threshold (POT) method for the prediction of short-term distributions of load extremes of offshore wind turbines. Such an optimal threshold level is found based on the estimation of the variance-to-mean ratio for the occurrence of peak values, which characterizes the Poisson assumption. A generalized Pareto distribution is then fitted to the extracted peaks over the optimal threshold level and the distribution parameters are estimated by the method of the maximum spacing estimation. This methodology is applied to estimate the short-term distributions of load extremes of the blade bending moment and the tower base bending moment at the mudline of a monopile-supported 5MW offshore wind turbine as an example. The accuracy of the POT method using the optimal threshold level is shown to be better, in terms of the distribution fitting, than that of the POT methods using empirical threshold levels. The comparisons among the short-term extreme response values predicted by using the POT method with the optimal threshold levels and with the empirical threshold levels and by using direct simulation results further substantiate the validity of the proposed new methodology.展开更多
The experiential adjustment process in an experiment on the ion source of the neutral beam injector system for the HT-7 Tokamak is reported in this paper. With regard to the data obtained in the same condition, in arr...The experiential adjustment process in an experiment on the ion source of the neutral beam injector system for the HT-7 Tokamak is reported in this paper. With regard to the data obtained in the same condition, in arranging the arc current intensities of every shot with a decay rank, the distributions of the arc current intensity correspond to the power laws, and the distribution obtained in the condition with the cryo-pump corresponds to the double Pareto distribution. Using the similar study method, the distributions of the arc duration are close to the power laws too. These power law distributions are formed rather naturally instead of being the results of purposeful seeking.展开更多
The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent and non-identical exponentiated Pareto distributed random variables with progressively censored sch...The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent and non-identical exponentiated Pareto distributed random variables with progressively censored scheme.Different interval estimations are proposed.The interval estimations obtained are exact,approximate and bootstrap confidence intervals.Different methods and the corresponding confidence intervals are compared using Monte-Carlo simulations.Simulation results show that the confidence intervals(CIs)of exact and approximate methods are really better than those of the bootstrap method.展开更多
It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV (Generalized Extreme Values) distribution can be derived from GPD (Generalized Pareto Distribution). Afterw...It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV (Generalized Extreme Values) distribution can be derived from GPD (Generalized Pareto Distribution). Afterwards, a quantile of extreme rainfall events in a certain return period is found using L-moment estimation and extreme rainfall events simulated by GPD and GEV, with all aspects of their results compared. Numerical simulations show that POT (Peaks Over Threshold)-based GPD is advantageous in its simple operation and subjected to practically no effect of the sample size of the primitive series, producing steady high-precision fittings in the whole field of values (including the high-end heavy tailed). In comparison, BM (Block Maximum)-based GEV is limited, to some extent, to the probability and quantile simulation, thereby showing that GPD is an extension of GEV, the former being of greater utility and higher significance to climate research compared to the latter.展开更多
The analysis and design of offshore structures necessitates the consideration of wave loads. Realistic modeling of wave loads is particularly important to ensure reliable performance of these structures. Among the ava...The analysis and design of offshore structures necessitates the consideration of wave loads. Realistic modeling of wave loads is particularly important to ensure reliable performance of these structures. Among the available methods for the modeling of the extreme significant wave height on a statistical basis, the peak over threshold method has attracted most attention. This method employs Poisson process to character- ize time-varying properties in the parameters of an extreme value distribution. In this paper, the peak over threshold method is reviewed and extended to account for subjectivity in the modeling. The freedom in selecting the threshold and the time span to separate extremes from the original time series data is incorpo- rated as imprecision in the model. This leads to an extension from random variables to random sets in the probabilistic model for the extreme significant wave height. The extended model is also applied to different periods of the sampled data to evaluate the significance of the climatic conditions on the uncertainties of the parameters.展开更多
Multiplicative multifractal process could well modal video traffic. The multiplier distributions in the multiplicatire multifractal model for video traffic are investigated and it is found that Gaussian is not suitabl...Multiplicative multifractal process could well modal video traffic. The multiplier distributions in the multiplicatire multifractal model for video traffic are investigated and it is found that Gaussian is not suitable for describing the multipliers on the small time scales. A new statistical distribution-symmetric Pareto distribution is introduced. It is applied instead of Gaussian for the multipliers on those scales. Based on that, the algorithm is updated so that symmetric pareto distribution and Gaussian distribution are used to model video traffic but on different time scales. The simulation results demonstrate that the algorithm could model video traffic more accurately.展开更多
This paper utilizes a change-point estimator based on <span>the </span><span style="font-style:italic;">φ</span><span>-</span><span>divergence. Since </span>&...This paper utilizes a change-point estimator based on <span>the </span><span style="font-style:italic;">φ</span><span>-</span><span>divergence. Since </span><span "=""><span>we seek a </span><span>near perfect</span><span> translation to reality, then locations of parameter change within a finite set of data have to be accounted for since the assumption of </span><span>stationary</span><span> model is too restrictive especially for long time series. The estimator is shown to be consistent through asymptotic theory and finally proven through simulations. The estimator is applied to the generalized Pareto distribution to estimate changes in the scale and shape parameters.</span></span>展开更多
We present a novel method to analyze extreme events of flows over manifolds called Peaks Over Manifold (POM). Here we show that under general and realistic hypotheses, the distribution of affectation measures converge...We present a novel method to analyze extreme events of flows over manifolds called Peaks Over Manifold (POM). Here we show that under general and realistic hypotheses, the distribution of affectation measures converges to a Generalized Pareto Distribution (GPD). The method is applicable to floods, ice cover extent, extreme rainfall or marine heatwaves. We present an application to a synthetic data set on tide height and to real ice cover data in Antartica.展开更多
A non-traditional fuzzy quantification method is presented in the modeling of an extreme significant wave height. First, a set of parametric models are selected to fit time series data for the significant wave height ...A non-traditional fuzzy quantification method is presented in the modeling of an extreme significant wave height. First, a set of parametric models are selected to fit time series data for the significant wave height and the extrapolation for extremes are obtained based on high quantile estimations. The quality of these results is compared and discussed. Then, the proposed fuzzy model, which combines Poisson process and gener-alized Pareto distribution (GPD) model, is applied to characterizing the wave extremes in the time series data. The estimations for a long-term return value are considered as time-varying as a threshold is regarded as non-stationary. The estimated intervals coupled with the fuzzy theory are then introduced to construct the probability bounds for the return values. This nontraditional model is analyzed in comparison with the traditional model in the degree of conservatism for the long-term estimate. The impact on the fuzzy bounds of extreme estimations from the non stationary effect in the proposed model is also investigated.展开更多
In this paper we first consider a risk process in which claim inter-arrival times and the time until the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate rui...In this paper we first consider a risk process in which claim inter-arrival times and the time until the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate ruin, given an initial reserve of u when the claim size follows a Pareto distribution. Follow Ramsay[8], Laplace transforms and exponential integrals are used to derive the solution, which involves a single integral of real valued functions along the positive real line, and the integrand is not of an oscillating kind. Then we show that the ultimate ruin probability can be expressed as the sum of expected values of functions of two different Gamma random variables. Finally, the results are extended to the Erlang(n) case. Numerical examples are given to illustrate the main results.展开更多
In this paper,some laws of large numbers are established for random variables that satisfy the Pareto distribution,so that the relevant conclusions in the traditional probability space are extended to the sub-linear e...In this paper,some laws of large numbers are established for random variables that satisfy the Pareto distribution,so that the relevant conclusions in the traditional probability space are extended to the sub-linear expectation space.Based on the Pareto distribution,we obtain the weak law of large numbers and strong law of large numbers of the weighted sum of some independent random variable sequences.展开更多
Gigacycle fatigue behavior of 60Si2CrVA high strength spring steel was investigated by ultrasonic fatigue test machine. Fatigue fractography was observed by scanning electron microscopy (SEM). Maximum inclusion size...Gigacycle fatigue behavior of 60Si2CrVA high strength spring steel was investigated by ultrasonic fatigue test machine. Fatigue fractography was observed by scanning electron microscopy (SEM). Maximum inclusion sizes and fatigue strength in different volumes were estimated by statistics of extreme values (SEV) and generalized Pareto distribution (GPD) methods. The results showed that S N curves of 60Si2CrVA spring steels for two rolling processes were not horizontal asymptotes but a gradient in a regime of 109 cycles, and traditional fatigue limits were eliminated. Surface machined topography and inclusions in steel were major factors that led to elimination of fatigue limit for 60Si2CrVA spring steel. The SEV and GPD methods could effectively predict size of the maximum inclusion and fatigue strength in different volumes of 60Si2CrVA spring steel. Predicted fatigue strength was in accordance with experimental results by ultrasonic fatigue testing.展开更多
The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley...The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley's K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong "roll-off" effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size (metal tonnage) is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.展开更多
A multi-status Markov chain model is proposed to produce daily rainfall, and based on which extreme rainfall is simulated with the generalized Pareto distribution (GPD). The simulated daily rainfall shows high preci...A multi-status Markov chain model is proposed to produce daily rainfall, and based on which extreme rainfall is simulated with the generalized Pareto distribution (GPD). The simulated daily rainfall shows high precision at most stations, especially in pluvial regions of East China. The analysis reveals that the multi- status Markov chain model excels the bi-status Markov chain model in simulating climatic features of extreme rainfall. Results from the selected six stations demonstrate excellent simulations in the following aspects: standard deviation of monthly precipitation, daily maximum precipitation, the monthly mean rainfall days, standard deviation of daily precipitation and mean daily precipitation, which are proved to be consistent with the observations. A comparative study involving 78 stations in East China also reveals good consistency in monthly mean rainfall days and mean daily maximum rainfall, except mean daily rainfall. Simulation results at the above 6 stations have shown satisfactory fitting capability of the extreme precipitation GPD method. Good analogy is also found between simulation and observation in threshold and return values. As the errors of the threshold decrease, so do the differences between the return and real values. All the above demonstrates the applicability of the Markov chain model to extreme rainfall simulations.展开更多
I use extreme values theory and data on influenza mortality from the U.S.for 1900 to 2018 to estimate the tail risks of mortality.I find that the distribution for influenza mortality rates is heavy-tailed,which sugges...I use extreme values theory and data on influenza mortality from the U.S.for 1900 to 2018 to estimate the tail risks of mortality.I find that the distribution for influenza mortality rates is heavy-tailed,which suggests that the tails of the mortality distribution are more informative than the events of high frequency(i.e.,years of low mortality).I also discuss the implications of my estimates for risk management and pandemic planning.展开更多
文摘How to choose an optimal threshold is a key problem in the generalized Pareto distribution (GPD) model. This paper attains the exact threshold by testing for GPD,and shows that GPD model allows the actuary to easily estimate high quantiles and the probable maximum loss from the medical insurance claims data.
文摘The generalized Pareto distribution model is a kind of hydrocarbon pool size probability statistical method for resource assessment. By introducing the time variable, resource conversion rate and the geological variable, resource density, such model can describe not only different types of basins, but also any exploration samples at different phases of exploration, up to the parent population. It is a dynamic distribution model with profound geological significance and wide applicability. Its basic principle and the process of resource assessment are described in this paper. The petroleum accumulation system is an appropriate assessment unit for such method. The hydrocarbon resource structure of the Huanghua Depression in Bohai Bay Basin was predicted by using this model. The prediction results accord with the knowledge of exploration in the Huanghua Depression, and point out the remaining resources potential and structure of different petroleum accumulation systems, which are of great significance for guiding future exploration in the Huanghua Depression.
基金Supported by Foundation of Ministry of Education of China(13YJC910005,13YJC910010,12YJA910005)Zhejiang Provincial Natural Science Foundation of China(LY16G020003)+2 种基金the Philosophy and Social Science Research Project in Zhejiang Province of China(13NDJC055YB)the National Natural Science Foundation of China(11371322)the Zhejiang Provincial Key Research Base for Humanities and Social Science Research(Statistics)
文摘The Pareto distribution plays an important role in various areas of research. In this paper, the average run length (ARL) unbiased control charts, which monitor the shape and threshold parameters of the Pareto distribution respectively, are proposed when the incontrol parameters are known. The effects of parameter estimation on the performance of the proposed control charts are also studied. Results show that the control charts with the estimated parameters are not suitable to be used in the known parameter case, thus the ARL-unbiased control charts for the shape and threshold parameters with the desired ARLo, which consider the variability of the parameter estimates, are further developed. The performance of the proposed control charts is investigated in terms of the ARL. Finally, an example is given to illustrate the proposed control charts.
基金supported by the funding of an independent research project from the Chinese State Key Laboratory of Ocean Engineering(Grant No.GKZD010038)
文摘This paper proposes a new methodology to select an optimal threshold level to be used in the peak over threshold (POT) method for the prediction of short-term distributions of load extremes of offshore wind turbines. Such an optimal threshold level is found based on the estimation of the variance-to-mean ratio for the occurrence of peak values, which characterizes the Poisson assumption. A generalized Pareto distribution is then fitted to the extracted peaks over the optimal threshold level and the distribution parameters are estimated by the method of the maximum spacing estimation. This methodology is applied to estimate the short-term distributions of load extremes of the blade bending moment and the tower base bending moment at the mudline of a monopile-supported 5MW offshore wind turbine as an example. The accuracy of the POT method using the optimal threshold level is shown to be better, in terms of the distribution fitting, than that of the POT methods using empirical threshold levels. The comparisons among the short-term extreme response values predicted by using the POT method with the optimal threshold levels and with the empirical threshold levels and by using direct simulation results further substantiate the validity of the proposed new methodology.
基金Meg-science Engineering Project of the Chinese Academy of Sciences
文摘The experiential adjustment process in an experiment on the ion source of the neutral beam injector system for the HT-7 Tokamak is reported in this paper. With regard to the data obtained in the same condition, in arranging the arc current intensities of every shot with a decay rank, the distributions of the arc current intensity correspond to the power laws, and the distribution obtained in the condition with the cryo-pump corresponds to the double Pareto distribution. Using the similar study method, the distributions of the arc duration are close to the power laws too. These power law distributions are formed rather naturally instead of being the results of purposeful seeking.
基金Natural Science Foundation of Guangdong Province,China(No.2018A030313829)Characteristic Innovation Projects of Ordinary Universities of Guangdong Province,China(No.2019KTSCX202)+1 种基金Higher Education Teaching Reform Project of Guangdong Province,China(No.2019625)Zhaoqing Educational Development Research Institute Project,China(No.ZQJYY2019033)。
文摘The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent and non-identical exponentiated Pareto distributed random variables with progressively censored scheme.Different interval estimations are proposed.The interval estimations obtained are exact,approximate and bootstrap confidence intervals.Different methods and the corresponding confidence intervals are compared using Monte-Carlo simulations.Simulation results show that the confidence intervals(CIs)of exact and approximate methods are really better than those of the bootstrap method.
基金supported jointly Science Foundation of China (Grant No. 40675043) Program of the Jiangsu Key Laboratory of Meteorological Disaster (Grant No. KLME050209).
文摘It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV (Generalized Extreme Values) distribution can be derived from GPD (Generalized Pareto Distribution). Afterwards, a quantile of extreme rainfall events in a certain return period is found using L-moment estimation and extreme rainfall events simulated by GPD and GEV, with all aspects of their results compared. Numerical simulations show that POT (Peaks Over Threshold)-based GPD is advantageous in its simple operation and subjected to practically no effect of the sample size of the primitive series, producing steady high-precision fittings in the whole field of values (including the high-end heavy tailed). In comparison, BM (Block Maximum)-based GEV is limited, to some extent, to the probability and quantile simulation, thereby showing that GPD is an extension of GEV, the former being of greater utility and higher significance to climate research compared to the latter.
基金The Singapore Ministry of Education AcRF Project under contract NTU ref:RF20/10
文摘The analysis and design of offshore structures necessitates the consideration of wave loads. Realistic modeling of wave loads is particularly important to ensure reliable performance of these structures. Among the available methods for the modeling of the extreme significant wave height on a statistical basis, the peak over threshold method has attracted most attention. This method employs Poisson process to character- ize time-varying properties in the parameters of an extreme value distribution. In this paper, the peak over threshold method is reviewed and extended to account for subjectivity in the modeling. The freedom in selecting the threshold and the time span to separate extremes from the original time series data is incorpo- rated as imprecision in the model. This leads to an extension from random variables to random sets in the probabilistic model for the extreme significant wave height. The extended model is also applied to different periods of the sampled data to evaluate the significance of the climatic conditions on the uncertainties of the parameters.
文摘Multiplicative multifractal process could well modal video traffic. The multiplier distributions in the multiplicatire multifractal model for video traffic are investigated and it is found that Gaussian is not suitable for describing the multipliers on the small time scales. A new statistical distribution-symmetric Pareto distribution is introduced. It is applied instead of Gaussian for the multipliers on those scales. Based on that, the algorithm is updated so that symmetric pareto distribution and Gaussian distribution are used to model video traffic but on different time scales. The simulation results demonstrate that the algorithm could model video traffic more accurately.
文摘This paper utilizes a change-point estimator based on <span>the </span><span style="font-style:italic;">φ</span><span>-</span><span>divergence. Since </span><span "=""><span>we seek a </span><span>near perfect</span><span> translation to reality, then locations of parameter change within a finite set of data have to be accounted for since the assumption of </span><span>stationary</span><span> model is too restrictive especially for long time series. The estimator is shown to be consistent through asymptotic theory and finally proven through simulations. The estimator is applied to the generalized Pareto distribution to estimate changes in the scale and shape parameters.</span></span>
文摘We present a novel method to analyze extreme events of flows over manifolds called Peaks Over Manifold (POM). Here we show that under general and realistic hypotheses, the distribution of affectation measures converges to a Generalized Pareto Distribution (GPD). The method is applicable to floods, ice cover extent, extreme rainfall or marine heatwaves. We present an application to a synthetic data set on tide height and to real ice cover data in Antartica.
文摘A non-traditional fuzzy quantification method is presented in the modeling of an extreme significant wave height. First, a set of parametric models are selected to fit time series data for the significant wave height and the extrapolation for extremes are obtained based on high quantile estimations. The quality of these results is compared and discussed. Then, the proposed fuzzy model, which combines Poisson process and gener-alized Pareto distribution (GPD) model, is applied to characterizing the wave extremes in the time series data. The estimations for a long-term return value are considered as time-varying as a threshold is regarded as non-stationary. The estimated intervals coupled with the fuzzy theory are then introduced to construct the probability bounds for the return values. This nontraditional model is analyzed in comparison with the traditional model in the degree of conservatism for the long-term estimate. The impact on the fuzzy bounds of extreme estimations from the non stationary effect in the proposed model is also investigated.
基金Supported by Postdoctoral Scientific Foundation of China,a CRGC grant from the University of Hong Kong and a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China (Project No.HKU 7139/01H).
文摘In this paper we first consider a risk process in which claim inter-arrival times and the time until the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate ruin, given an initial reserve of u when the claim size follows a Pareto distribution. Follow Ramsay[8], Laplace transforms and exponential integrals are used to derive the solution, which involves a single integral of real valued functions along the positive real line, and the integrand is not of an oscillating kind. Then we show that the ultimate ruin probability can be expressed as the sum of expected values of functions of two different Gamma random variables. Finally, the results are extended to the Erlang(n) case. Numerical examples are given to illustrate the main results.
基金AcknowledgmentssThe authors thank the National Natural Science Foundation of China(Grant No.12061028)Guangxi Natural Science Foundation Joint Incubation Project(Grant No.2018GXNSFAA294131)+1 种基金Guangxi Natural Science Foundation(Grant No.2018G XNSFAA281011)Innovation Project of Guangxi Graduate Education(Grant No.YCSW2020175)for their financial support。
文摘In this paper,some laws of large numbers are established for random variables that satisfy the Pareto distribution,so that the relevant conclusions in the traditional probability space are extended to the sub-linear expectation space.Based on the Pareto distribution,we obtain the weak law of large numbers and strong law of large numbers of the weighted sum of some independent random variable sequences.
基金Sponsored by National Basic Research Program(973 Program)of China(2004CB619100)
文摘Gigacycle fatigue behavior of 60Si2CrVA high strength spring steel was investigated by ultrasonic fatigue test machine. Fatigue fractography was observed by scanning electron microscopy (SEM). Maximum inclusion sizes and fatigue strength in different volumes were estimated by statistics of extreme values (SEV) and generalized Pareto distribution (GPD) methods. The results showed that S N curves of 60Si2CrVA spring steels for two rolling processes were not horizontal asymptotes but a gradient in a regime of 109 cycles, and traditional fatigue limits were eliminated. Surface machined topography and inclusions in steel were major factors that led to elimination of fatigue limit for 60Si2CrVA spring steel. The SEV and GPD methods could effectively predict size of the maximum inclusion and fatigue strength in different volumes of 60Si2CrVA spring steel. Predicted fatigue strength was in accordance with experimental results by ultrasonic fatigue testing.
基金supported by Geological Survey of Canada and China University of Geosciences (Wuhan)
文摘The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley's K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong "roll-off" effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size (metal tonnage) is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.
基金the National Natural Science Foundation of China under Grant No.40875058the Major Fundamental Research Program of Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant No.07KJA17020.
文摘A multi-status Markov chain model is proposed to produce daily rainfall, and based on which extreme rainfall is simulated with the generalized Pareto distribution (GPD). The simulated daily rainfall shows high precision at most stations, especially in pluvial regions of East China. The analysis reveals that the multi- status Markov chain model excels the bi-status Markov chain model in simulating climatic features of extreme rainfall. Results from the selected six stations demonstrate excellent simulations in the following aspects: standard deviation of monthly precipitation, daily maximum precipitation, the monthly mean rainfall days, standard deviation of daily precipitation and mean daily precipitation, which are proved to be consistent with the observations. A comparative study involving 78 stations in East China also reveals good consistency in monthly mean rainfall days and mean daily maximum rainfall, except mean daily rainfall. Simulation results at the above 6 stations have shown satisfactory fitting capability of the extreme precipitation GPD method. Good analogy is also found between simulation and observation in threshold and return values. As the errors of the threshold decrease, so do the differences between the return and real values. All the above demonstrates the applicability of the Markov chain model to extreme rainfall simulations.
文摘I use extreme values theory and data on influenza mortality from the U.S.for 1900 to 2018 to estimate the tail risks of mortality.I find that the distribution for influenza mortality rates is heavy-tailed,which suggests that the tails of the mortality distribution are more informative than the events of high frequency(i.e.,years of low mortality).I also discuss the implications of my estimates for risk management and pandemic planning.