Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In thi...Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In this paper, we mainly consider these problems in general random effect model with balanced data. Exact tests and confidence intervals for a single variance component corresponding to random effect are developed by using generalized p-values and generalized confidence intervals. The resulting procedures are easy to compute and are applicable to small samples. Exact tests and confidence intervals are also established for comparing the random-effects variance components and the sum of random-effects variance components in two independent general random effect models with balanced data. Furthermore, we investigate the statistical properties of the resulting tests. Finally, some simulation results on the type Ⅰ error probability and power of the proposed test are reported. The simulation results indicate that exact test is extremely satisfactory for controlling type Ⅰ error probability.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
This paper provides a general method for constructing generalized p-value via the fiducial inference.Furthermore,the power properties of the generalized test are discussed.As illustrations, the two-parameter exponenti...This paper provides a general method for constructing generalized p-value via the fiducial inference.Furthermore,the power properties of the generalized test are discussed.As illustrations, the two-parameter exponential distribution and unbalanced two-fold nested design are researched.It is shown that the resulting generalized p-values are of good frequency property.展开更多
In this paper, the interval estimation and hypothesis testing of the mixing proportion in mixture distributions are considered. A statistical inferential method is proposed which is inspired by the generalized p-value...In this paper, the interval estimation and hypothesis testing of the mixing proportion in mixture distributions are considered. A statistical inferential method is proposed which is inspired by the generalized p-values and generalized pivotal quantity. In some situations, the true levels of the tests given in the paper are equal to nominal levels, and the true coverage of the interval estimation or confidence bounds is also equal to nominal one. In other situations, under mild conditions, the tests are consistent and the coverage of the interval estimations or the confidence bounds is asymptotically equal to nominal coverage. Meanwhile, some simulations are performed which show that our method is satisfactory.展开更多
The authors discuss the unbalanced two-way ANOVA model under heteroscedasticity. By taking the generalized approach, the authors derive the generalized p-values for testing the equality of fixed effects and the genera...The authors discuss the unbalanced two-way ANOVA model under heteroscedasticity. By taking the generalized approach, the authors derive the generalized p-values for testing the equality of fixed effects and the generalized confidence regions for these effects. The authors also provide their frequentist properties in large-sample cases. Simulation studies show that the generalized confidence regions have good coverage probabilities.展开更多
In this paper,based on physics-informed neural networks(PINNs),a good deep learning neural network framework that can be used to effectively solve the nonlinear evolution partial differential equations(PDEs)and other ...In this paper,based on physics-informed neural networks(PINNs),a good deep learning neural network framework that can be used to effectively solve the nonlinear evolution partial differential equations(PDEs)and other types of nonlinear physical models,we study the nonlinear Schrodinger equation(NLSE)with the generalized PT-symmetric Scarf-Ⅱpotential,which is an important physical model in many fields of nonlinear physics.Firstly,we choose three different initial values and the same Dinchlet boundaiy conditions to solve the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential via the PINN deep learning method,and the obtained results are compared with ttose denved by the toditional numencal methods.Then,we mvestigate effect of two factors(optimization steps and activation functions)on the performance of the PINN deep learning method in the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential.Ultimately,the data-driven coefficient discovery of the generalized PT-symmetric Scarf-Ⅱpotential or the dispersion and nonlinear items of the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential can be approximately ascertained by using the PINN deep learning method.Our results may be meaningful for further investigation of the nonlinear Schrodmger equation with the generalized PT-symmetric Scarf-Ⅱpotential in the deep learning.展开更多
Standardized Precipitation Index(SPI)and Standardized Precipitation Evapotranspiration Index(SPEI),traditionally derived at a monthly scale,are widely used drought indices.To overcome temporalresolution limitations,we...Standardized Precipitation Index(SPI)and Standardized Precipitation Evapotranspiration Index(SPEI),traditionally derived at a monthly scale,are widely used drought indices.To overcome temporalresolution limitations,we have previously developed and published a well-validated daily SPI/SPEI in situ dataset.Although having a high temporal resolution,this in situ dataset presents low spatial resolution due to the scarcity of stations.Therefore,based on the China Meteorological Forcing Dataset,which is composed of data from more than 1,000 ground-based observation sites and multiple remote sensing grid meteorological dataset,we present the first high spatiotemporal-resolution daily SPI/SPEI raster datasets over China.It spans from 1979 to 2018,with a spatial resolution of 0.1°×0.1°,a temporal resolution of 1-day,and the timescales of 30-,90-,and 360-days.Results show that the spatial distributions of drought event characteristics detected by the daily SPI/SPEI are consistent with the monthly SPI/SPEI.The correlation between the daily value of the 12-month scale and the monthly value of SPI/SPEI is the strongest,with linear correlation,Nash-Sutcliffe coefficient,and normalized root mean square error of 0.98,0.97,and 0.04,respectively.The daily SPI/SPEI is shown to be more sensitive to flash drought than the monthly SPI/SPEI.Our improved SPI/SPEI shows high accuracy and credibility,presenting enhanced results when compared to the monthly SPI/SPEI.The total data volume is up to 150 GB,compressed to 91 GB in Network Common Data Form(NetCDF).It can be available from Figshare(https://doi.org/10.6084/m9.figshare.c.5823533)and ScienceDB(https://doi.org/10.57760/sciencedb.j00076.00103).展开更多
This paper is mainly to discuss cooperative games on convex geometries with a coalition structure, which can be seen as an extension of cooperative games with a coalition structure. For this kind of games, the coopera...This paper is mainly to discuss cooperative games on convex geometries with a coalition structure, which can be seen as an extension of cooperative games with a coalition structure. For this kind of games, the cooperation among unions and within each union will be the convex sets, i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively. The explicit form of the generalized Owen value for this kind of games is given, which can be seen as an extension of the Owen value. Eklrthermore, two special cases of this kind of games are researched. The corresponding Davoff indices are also stHdied. Fin~.llv ~n ilhl^r~＇i, ~r^l~ to ~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
In this paper, we consider a double compound Poisson risk model involving two independent classes ofinsurance risks with a threshold dividend strategy. We derived the integro-differential equations （IDE） with certai...In this paper, we consider a double compound Poisson risk model involving two independent classes ofinsurance risks with a threshold dividend strategy. We derived the integro-differential equations （IDE） with certain boundary conditions for the present value of dividends until ruin. When the claims from both classes are exponentially distributed, we show that the threshold dividend strategy is an optimal dividend strategy.展开更多
Feature information extraction is one of the key steps in prognostics and health management of rotating machinery.In the present study,an investigation about the feasibility of a methodology based on generalized S tra...Feature information extraction is one of the key steps in prognostics and health management of rotating machinery.In the present study,an investigation about the feasibility of a methodology based on generalized S transform(GST)and singular value decomposition(SVD)methods for feature extraction in rolling bearing,due to local damage under variable conditions,is conducted.The technique adopts the GST method,following the time-frequency analysis,to transform a raw fault signal of the rolling bearing into a two-dimensional complex matrix.And then,the SVD method is performed to decompose the matrix to obtain the feature vectors.By this procedure it is possible to obtain the fault feature information of rolling bearing under different speeds and different loads.In order to streamline the feature parameters of the feature vectors to train more uncomplicated models,the principal component analysis(PCA)subsequently performed.The particle swarm optimization-support vector machine(PSO-SVM)model is used to identify and classify the different fault states of rolling bearing.Furthermore,in order to highlight the superiority of the proposed method some comparisons are conducted with the conventional methods.The obtained results show that the proposed method can effectively extract fault features of the rolling bearing under variable conditions.展开更多
文摘Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In this paper, we mainly consider these problems in general random effect model with balanced data. Exact tests and confidence intervals for a single variance component corresponding to random effect are developed by using generalized p-values and generalized confidence intervals. The resulting procedures are easy to compute and are applicable to small samples. Exact tests and confidence intervals are also established for comparing the random-effects variance components and the sum of random-effects variance components in two independent general random effect models with balanced data. Furthermore, we investigate the statistical properties of the resulting tests. Finally, some simulation results on the type Ⅰ error probability and power of the proposed test are reported. The simulation results indicate that exact test is extremely satisfactory for controlling type Ⅰ error probability.
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.
基金This work was partly supported by the National Natural Science Foundation of China(Grant Nos.10271013,30600119 and 90403130)the Fund of Shandong University of Technology(Grant Nos.2006KJZ01,2005KJM18)
文摘This paper provides a general method for constructing generalized p-value via the fiducial inference.Furthermore,the power properties of the generalized test are discussed.As illustrations, the two-parameter exponential distribution and unbalanced two-fold nested design are researched.It is shown that the resulting generalized p-values are of good frequency property.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10271013, 10771015)
文摘In this paper, the interval estimation and hypothesis testing of the mixing proportion in mixture distributions are considered. A statistical inferential method is proposed which is inspired by the generalized p-values and generalized pivotal quantity. In some situations, the true levels of the tests given in the paper are equal to nominal levels, and the true coverage of the interval estimation or confidence bounds is also equal to nominal one. In other situations, under mild conditions, the tests are consistent and the coverage of the interval estimations or the confidence bounds is asymptotically equal to nominal coverage. Meanwhile, some simulations are performed which show that our method is satisfactory.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos.10771126 and 10771015.
文摘The authors discuss the unbalanced two-way ANOVA model under heteroscedasticity. By taking the generalized approach, the authors derive the generalized p-values for testing the equality of fixed effects and the generalized confidence regions for these effects. The authors also provide their frequentist properties in large-sample cases. Simulation studies show that the generalized confidence regions have good coverage probabilities.
基金supported by the National Natural Science Foundation of China under Grant Nos.11775121,11435005the K.C.Wong Magna Fund of Ningbo University。
文摘In this paper,based on physics-informed neural networks(PINNs),a good deep learning neural network framework that can be used to effectively solve the nonlinear evolution partial differential equations(PDEs)and other types of nonlinear physical models,we study the nonlinear Schrodinger equation(NLSE)with the generalized PT-symmetric Scarf-Ⅱpotential,which is an important physical model in many fields of nonlinear physics.Firstly,we choose three different initial values and the same Dinchlet boundaiy conditions to solve the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential via the PINN deep learning method,and the obtained results are compared with ttose denved by the toditional numencal methods.Then,we mvestigate effect of two factors(optimization steps and activation functions)on the performance of the PINN deep learning method in the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential.Ultimately,the data-driven coefficient discovery of the generalized PT-symmetric Scarf-Ⅱpotential or the dispersion and nonlinear items of the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential can be approximately ascertained by using the PINN deep learning method.Our results may be meaningful for further investigation of the nonlinear Schrodmger equation with the generalized PT-symmetric Scarf-Ⅱpotential in the deep learning.
基金the China meteorological forcing dataset.Thanks to the Natural Science Foundation of Fujian Province(No.2021J01627,No.2020J01465)the National Natural Science Foundation of China(No.41601562,No.32071776)for their financial support.
文摘Standardized Precipitation Index(SPI)and Standardized Precipitation Evapotranspiration Index(SPEI),traditionally derived at a monthly scale,are widely used drought indices.To overcome temporalresolution limitations,we have previously developed and published a well-validated daily SPI/SPEI in situ dataset.Although having a high temporal resolution,this in situ dataset presents low spatial resolution due to the scarcity of stations.Therefore,based on the China Meteorological Forcing Dataset,which is composed of data from more than 1,000 ground-based observation sites and multiple remote sensing grid meteorological dataset,we present the first high spatiotemporal-resolution daily SPI/SPEI raster datasets over China.It spans from 1979 to 2018,with a spatial resolution of 0.1°×0.1°,a temporal resolution of 1-day,and the timescales of 30-,90-,and 360-days.Results show that the spatial distributions of drought event characteristics detected by the daily SPI/SPEI are consistent with the monthly SPI/SPEI.The correlation between the daily value of the 12-month scale and the monthly value of SPI/SPEI is the strongest,with linear correlation,Nash-Sutcliffe coefficient,and normalized root mean square error of 0.98,0.97,and 0.04,respectively.The daily SPI/SPEI is shown to be more sensitive to flash drought than the monthly SPI/SPEI.Our improved SPI/SPEI shows high accuracy and credibility,presenting enhanced results when compared to the monthly SPI/SPEI.The total data volume is up to 150 GB,compressed to 91 GB in Network Common Data Form(NetCDF).It can be available from Figshare(https://doi.org/10.6084/m9.figshare.c.5823533)and ScienceDB(https://doi.org/10.57760/sciencedb.j00076.00103).
基金supported by the National Natural Science Foundation of China under Grant Nos.71201089, 71271217,and 71071018the Natural Science Foundation of Shandong Province,China,under Grant No. ZR2012GQ005
文摘This paper is mainly to discuss cooperative games on convex geometries with a coalition structure, which can be seen as an extension of cooperative games with a coalition structure. For this kind of games, the cooperation among unions and within each union will be the convex sets, i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively. The explicit form of the generalized Owen value for this kind of games is given, which can be seen as an extension of the Owen value. Eklrthermore, two special cases of this kind of games are researched. The corresponding Davoff indices are also stHdied. Fin~.llv ~n ilhl^r~＇i, ~r^l~ to ~
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.
基金Supported by the Natural Science Foundation of Jiangxi Province (2008GQS0035)the Foundation of Zhejiang Provincial Education Department Research Projects (Y200803009)
文摘In this paper, we consider a double compound Poisson risk model involving two independent classes ofinsurance risks with a threshold dividend strategy. We derived the integro-differential equations （IDE） with certain boundary conditions for the present value of dividends until ruin. When the claims from both classes are exponentially distributed, we show that the threshold dividend strategy is an optimal dividend strategy.
基金Guangdong Provincial Natural Science Foundation of China(Grant No.2020B1515120006)Guangdong Innovation Team(Grant Nos.2020KCXTD015,2022KCXTD029)Guangdong Universities New Information Field(Grant No.2021ZDZX1057).
文摘Feature information extraction is one of the key steps in prognostics and health management of rotating machinery.In the present study,an investigation about the feasibility of a methodology based on generalized S transform(GST)and singular value decomposition(SVD)methods for feature extraction in rolling bearing,due to local damage under variable conditions,is conducted.The technique adopts the GST method,following the time-frequency analysis,to transform a raw fault signal of the rolling bearing into a two-dimensional complex matrix.And then,the SVD method is performed to decompose the matrix to obtain the feature vectors.By this procedure it is possible to obtain the fault feature information of rolling bearing under different speeds and different loads.In order to streamline the feature parameters of the feature vectors to train more uncomplicated models,the principal component analysis(PCA)subsequently performed.The particle swarm optimization-support vector machine(PSO-SVM)model is used to identify and classify the different fault states of rolling bearing.Furthermore,in order to highlight the superiority of the proposed method some comparisons are conducted with the conventional methods.The obtained results show that the proposed method can effectively extract fault features of the rolling bearing under variable conditions.
