A joint statistical model of wind speed and wind shear is critical for height-dependent wind resource characteristic analysis.However,given the different atmospheric conditions that may be involved,the statistical dis...A joint statistical model of wind speed and wind shear is critical for height-dependent wind resource characteristic analysis.However,given the different atmospheric conditions that may be involved,the statistical distribution of the two variables may show multimodal characteristics.In this work,a finite mixture bivariate statistical model was designed to describe the statistical properties,which is composed of several components,each with a Weibull distribution and a normal distribution for wind speed and wind shear,respectively,with a Gaussian copula to describe the dependency structure between the two variables.To confirm the developed model,reanalysis data from six positions in the coastal sea areas of China were used.Our results disclosed that the developed joint statistical model can accurately capture the different multimodal structures presented in all the bivariate samples under mixed atmospheric conditions,giving acceptable predictions of the joint probability distributions.Proper consideration of wind shear coefficient variation is crucial in estimating height-dependent wind resource characteristics.Importantly,unlike traditional methods that are limited to specific hub heights,the model developed here can estimate wind energy potential across different hub heights,enhancing the economic viability assessment of wind power projects.展开更多
In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar re...In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar remote sensing data and geographic information system(GIS), for landslide susceptibility mapping(LSM) in the Gorganroud watershed, Iran. Fifteen topographic, hydrological, geological and environmental conditioning factors and a landslide inventory(70%, or 298 landslides) were used in mapping. Phased array-type L-band synthetic aperture radar data were used to extract topographic parameters. Coefficients of tolerance and variance inflation factor were used to determine the coherence among conditioning factors. Data for the landslide inventory map were obtained from various resources, such as Iranian Landslide Working Party(ILWP), Forestry, Rangeland and Watershed Organisation(FRWO), extensive field surveys, interpretation of aerial photos and satellite images, and radar data. Of the total data, 30% were used to validate LSMs, using area under the curve(AUC), frequency ratio(FR) and seed cell area index(SCAI).Normalised difference vegetation index, land use/land cover and slope degree in BRT model elevation, rainfall and distance from stream were found to be important factors and were given the highest weightage in modelling. Validation results using AUC showed that the ensemble LNRF-BRT and LNRFLMR models(AUC = 0.912(91.2%) and 0.907(90.7%), respectively) had high predictive accuracy than the LNRF model alone(AUC = 0.855(85.5%)). The FR and SCAI analyses showed that all models divided the parameter classes with high precision. Overall, our novel approach of combining multivariate and machine learning methods with bivariate models, radar remote sensing data and GIS proved to be a powerful tool for landslide susceptibility mapping.展开更多
Testing-time when a change of a stochastic characteristic of the software failure-occurrence time or software failure-occurrence time-interval is observed is called change-point. It is said that effect of the change-p...Testing-time when a change of a stochastic characteristic of the software failure-occurrence time or software failure-occurrence time-interval is observed is called change-point. It is said that effect of the change-point on the software reliability growth process influences on accuracy for software reliability assessment based on a software reliability growth model (SRGM). We propose an SRGM with the effect of the change-point based on a bivariate SRGM, in which the software reliability growth process is assumed to depend on the testing-time and testing-effort factors simultaneously, for accurate software reliability assessment. And we discuss an optimal software release problem for deriving optimal testing-effort expenditures based on our model. Further, we show numerical examples of software reliability assessment based on our bivariate SRGM and estimation of optimal testing-effort expenditures by using actual data.展开更多
Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict o...Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.展开更多
A new covariate dependent zero-truncated bivariate Poisson model is proposed in this paper employing generalized linear model. A marginal-conditional approach is used to show the bivariate model. The proposed model wi...A new covariate dependent zero-truncated bivariate Poisson model is proposed in this paper employing generalized linear model. A marginal-conditional approach is used to show the bivariate model. The proposed model with estimation procedure and tests for goodness-of-fit and under (or over) dispersion are shown and applied to road safety data. Two correlated outcome variables considered in this study are number of cars involved in an accident and number of casualties for given number of cars.展开更多
In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heteroscedastic errors. We construct confidence intervals and median unbiased estimator ...In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heteroscedastic errors. We construct confidence intervals and median unbiased estimator for the parameter of interest. We show that the proposed estimator has better predictive potential than the usual least squares estimator via simulation. An empirical application to finance is given. And a possible extension of the estimation procedure to cointegration models is also described.展开更多
Modern highly reliable products may have two or more quality characteristics(QCs) because of their complex structures and abundant functions. Relations between the QCs should be considered when assessing the reliabili...Modern highly reliable products may have two or more quality characteristics(QCs) because of their complex structures and abundant functions. Relations between the QCs should be considered when assessing the reliability of these products. This paper conducts a Bayesian analysis for a bivariate constant-stress accelerated degradation model based on the inverse Gaussian(IG) process. We assume that the product considered has two QCs and each of the QCs is governed by an IG process. The relationship between the QCs is described by a Frank copula function. We also assume that the stress on the products affects not only the parameters of the IG processes, but also the parameter of the Frank copula function. The Bayesian MCMC method is developed to calculate the maximum likelihood estimators(MLE) of the model parameters. The reliability function and the mean-time-to-failure(MTTF) are estimated through the calculation of the posterior samples. Finally, a simulation example is presented to illustrate the proposed bivariate constant-stress accelerated degradation model.展开更多
Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the depend...Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the dependent competing risks model by using the Marshall-Olkin bivariate Weibull(MOBW) distribution.The maximum likelihood estimations(MLEs), midpoint approximation(MPA) estimations and approximate confidence intervals(ACIs) of the unknown parameters are obtained. In addition, the Bayes approach is also considered based on the Gamma-Dirichlet prior of the scale parameters, with the given shape parameter.The acceptance-rejection sampling method is used to obtain the Bayes estimations and construct credible intervals(CIs). Finally,two numerical examples are used to show the performance of the proposed methods.展开更多
Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rate...Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.展开更多
This paper discusses the model construction and the association between the Italy and the Germany＇s stock markets. The period of study data is from January 3, 2000 to June 30, 2008. This paper also utilizes Student＇...This paper discusses the model construction and the association between the Italy and the Germany＇s stock markets. The period of study data is from January 3, 2000 to June 30, 2008. This paper also utilizes Student＇s t distribution to analyze the proposed model. The empirical results show that the two stock markets are mutually affected each other, and the dynamic conditional correlation （DCC） and the bivariate asymmetric-GARCH （1, 2） model is appropriate in evaluating the relation between them. The empirical result also indicates that Italy and Germany＇s stock markets show a positive relationship. The average value of correlation coefficient equals to 0.8424, which implies that the two stock markets return volatility have a synchronized influence on each other. In addition, the empirical result also shows that there is an asymmetrical effect between Italy and the Germany＇s stock markets, and demonstrates that the good news and bad news of the stock returns＇ volatility will produce the different variation risks for Italy and the Germany＇s stock price markets.展开更多
In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type...In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.展开更多
In this paper,the Taixin Integrated Economic Zone in Shanxi Province is taken as the research object,and the coupling coordination degree model and bivariate spatial autocorrelation model are used to judge the couplin...In this paper,the Taixin Integrated Economic Zone in Shanxi Province is taken as the research object,and the coupling coordination degree model and bivariate spatial autocorrelation model are used to judge the coupling coordination and spatial-temporal correlation between urbanization and ecosystem service,and the hotspot analysis is used to judge the spatial-temporal trend of urbanization and ecosystem service.The results show that:(1)The urbanization level from 2000 to 2020 continued to rise,the areas with relatively high urbanization were concentrated in the central part of the study area,and the relatively high terrain areas on both sides of the study area,the urbanization was relatively slow,and the hotspot areas with highly significant and significant urbanization level from 2000 to 2020 were distributed as bands in the central part of the study area and the area was rising,and there was no Cold spot area distribution;between 2000 and 2020,the ecosystem service value in the study area increased by 2.6800×10^(8) yuan.Over these two decades,it exhibited a development trend that first rose and then declined.The woodland and grassland agglomeration areas were located on the two sides of the study area,forming highly significant and significant hotspots.Conversely,the central and northeastern parts of the study area were characterized by concentrated man-made land surfaces and croplands,resulting in the formation of highly significant and significant cold spots.(2)In the central part of the study area where man-made land surface and cultivated land are concentrated,the coupling coordination between urbanization and ecosystem service is in the intermediate dislocation and mild dislocation interval;the woodland and grassland concentration areas on both sides of the study area are ecologically fragile,and the coupling coordination between the two is in the level of less than intermediate dislocation.(3)From 2000 to 2020,urbanization and the value of ecosystem services were both negatively correlated,although the correlation coefficient was low.In the central and northeastern parts,urbanization and ecosystem service exhibited patterns of high-low,high-high,and low-low clustering.Conversely,on both sides of the study area,most of the clusters showed a low-high pattern.展开更多
基金supported by the Key R&D Program of Shandong Province,China(No.2021ZLGX04)the National Natural Science Foundation of China(No.52171284)。
文摘A joint statistical model of wind speed and wind shear is critical for height-dependent wind resource characteristic analysis.However,given the different atmospheric conditions that may be involved,the statistical distribution of the two variables may show multimodal characteristics.In this work,a finite mixture bivariate statistical model was designed to describe the statistical properties,which is composed of several components,each with a Weibull distribution and a normal distribution for wind speed and wind shear,respectively,with a Gaussian copula to describe the dependency structure between the two variables.To confirm the developed model,reanalysis data from six positions in the coastal sea areas of China were used.Our results disclosed that the developed joint statistical model can accurately capture the different multimodal structures presented in all the bivariate samples under mixed atmospheric conditions,giving acceptable predictions of the joint probability distributions.Proper consideration of wind shear coefficient variation is crucial in estimating height-dependent wind resource characteristics.Importantly,unlike traditional methods that are limited to specific hub heights,the model developed here can estimate wind energy potential across different hub heights,enhancing the economic viability assessment of wind power projects.
基金supported by the Centre for Advanced Modelling and Geospatial Information Systems(CAMGIS),UTS under grant numbers 321740.2232335,323930,and 321740.2232357
文摘In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar remote sensing data and geographic information system(GIS), for landslide susceptibility mapping(LSM) in the Gorganroud watershed, Iran. Fifteen topographic, hydrological, geological and environmental conditioning factors and a landslide inventory(70%, or 298 landslides) were used in mapping. Phased array-type L-band synthetic aperture radar data were used to extract topographic parameters. Coefficients of tolerance and variance inflation factor were used to determine the coherence among conditioning factors. Data for the landslide inventory map were obtained from various resources, such as Iranian Landslide Working Party(ILWP), Forestry, Rangeland and Watershed Organisation(FRWO), extensive field surveys, interpretation of aerial photos and satellite images, and radar data. Of the total data, 30% were used to validate LSMs, using area under the curve(AUC), frequency ratio(FR) and seed cell area index(SCAI).Normalised difference vegetation index, land use/land cover and slope degree in BRT model elevation, rainfall and distance from stream were found to be important factors and were given the highest weightage in modelling. Validation results using AUC showed that the ensemble LNRF-BRT and LNRFLMR models(AUC = 0.912(91.2%) and 0.907(90.7%), respectively) had high predictive accuracy than the LNRF model alone(AUC = 0.855(85.5%)). The FR and SCAI analyses showed that all models divided the parameter classes with high precision. Overall, our novel approach of combining multivariate and machine learning methods with bivariate models, radar remote sensing data and GIS proved to be a powerful tool for landslide susceptibility mapping.
文摘Testing-time when a change of a stochastic characteristic of the software failure-occurrence time or software failure-occurrence time-interval is observed is called change-point. It is said that effect of the change-point on the software reliability growth process influences on accuracy for software reliability assessment based on a software reliability growth model (SRGM). We propose an SRGM with the effect of the change-point based on a bivariate SRGM, in which the software reliability growth process is assumed to depend on the testing-time and testing-effort factors simultaneously, for accurate software reliability assessment. And we discuss an optimal software release problem for deriving optimal testing-effort expenditures based on our model. Further, we show numerical examples of software reliability assessment based on our bivariate SRGM and estimation of optimal testing-effort expenditures by using actual data.
文摘Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.
文摘A new covariate dependent zero-truncated bivariate Poisson model is proposed in this paper employing generalized linear model. A marginal-conditional approach is used to show the bivariate model. The proposed model with estimation procedure and tests for goodness-of-fit and under (or over) dispersion are shown and applied to road safety data. Two correlated outcome variables considered in this study are number of cars involved in an accident and number of casualties for given number of cars.
基金The NNSF(10571073)of china,and 985 project of Jilin University.
文摘In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heteroscedastic errors. We construct confidence intervals and median unbiased estimator for the parameter of interest. We show that the proposed estimator has better predictive potential than the usual least squares estimator via simulation. An empirical application to finance is given. And a possible extension of the estimation procedure to cointegration models is also described.
基金the National Natural Science Foundation of China(No.11671080)the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence(No.BM2017002)
文摘Modern highly reliable products may have two or more quality characteristics(QCs) because of their complex structures and abundant functions. Relations between the QCs should be considered when assessing the reliability of these products. This paper conducts a Bayesian analysis for a bivariate constant-stress accelerated degradation model based on the inverse Gaussian(IG) process. We assume that the product considered has two QCs and each of the QCs is governed by an IG process. The relationship between the QCs is described by a Frank copula function. We also assume that the stress on the products affects not only the parameters of the IG processes, but also the parameter of the Frank copula function. The Bayesian MCMC method is developed to calculate the maximum likelihood estimators(MLE) of the model parameters. The reliability function and the mean-time-to-failure(MTTF) are estimated through the calculation of the posterior samples. Finally, a simulation example is presented to illustrate the proposed bivariate constant-stress accelerated degradation model.
基金supported by the National Natural Science Foundation of China(71571144 71401134)the Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province(2016KW-033)
文摘Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the dependent competing risks model by using the Marshall-Olkin bivariate Weibull(MOBW) distribution.The maximum likelihood estimations(MLEs), midpoint approximation(MPA) estimations and approximate confidence intervals(ACIs) of the unknown parameters are obtained. In addition, the Bayes approach is also considered based on the Gamma-Dirichlet prior of the scale parameters, with the given shape parameter.The acceptance-rejection sampling method is used to obtain the Bayes estimations and construct credible intervals(CIs). Finally,two numerical examples are used to show the performance of the proposed methods.
文摘Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.
文摘This paper discusses the model construction and the association between the Italy and the Germany＇s stock markets. The period of study data is from January 3, 2000 to June 30, 2008. This paper also utilizes Student＇s t distribution to analyze the proposed model. The empirical results show that the two stock markets are mutually affected each other, and the dynamic conditional correlation （DCC） and the bivariate asymmetric-GARCH （1, 2） model is appropriate in evaluating the relation between them. The empirical result also indicates that Italy and Germany＇s stock markets show a positive relationship. The average value of correlation coefficient equals to 0.8424, which implies that the two stock markets return volatility have a synchronized influence on each other. In addition, the empirical result also shows that there is an asymmetrical effect between Italy and the Germany＇s stock markets, and demonstrates that the good news and bad news of the stock returns＇ volatility will produce the different variation risks for Italy and the Germany＇s stock price markets.
基金supported by the Natural Science Foundation of Guangdong(No.2024A1515010983)the project of Guangdong Province General Colleges and Universities with Special Characteristics and Innovations(No.2022KTSCX150)+2 种基金Zhaoqing Science and Technology Innovation Guidance Project(No.2023040317006)Zhaoqing Institute of Education Development Project(No.ZQJYY2023021)Zhaoqing College Quality Project and Teaching Reform Project(No.zlgc202112).
文摘In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.
基金supported by the Natural Science Foundation of Shanxi Province(Grant No.20210302124437)the Graduate Student Research and Innovation Project of Shanxi Province(Grant No.2023KY551).
文摘In this paper,the Taixin Integrated Economic Zone in Shanxi Province is taken as the research object,and the coupling coordination degree model and bivariate spatial autocorrelation model are used to judge the coupling coordination and spatial-temporal correlation between urbanization and ecosystem service,and the hotspot analysis is used to judge the spatial-temporal trend of urbanization and ecosystem service.The results show that:(1)The urbanization level from 2000 to 2020 continued to rise,the areas with relatively high urbanization were concentrated in the central part of the study area,and the relatively high terrain areas on both sides of the study area,the urbanization was relatively slow,and the hotspot areas with highly significant and significant urbanization level from 2000 to 2020 were distributed as bands in the central part of the study area and the area was rising,and there was no Cold spot area distribution;between 2000 and 2020,the ecosystem service value in the study area increased by 2.6800×10^(8) yuan.Over these two decades,it exhibited a development trend that first rose and then declined.The woodland and grassland agglomeration areas were located on the two sides of the study area,forming highly significant and significant hotspots.Conversely,the central and northeastern parts of the study area were characterized by concentrated man-made land surfaces and croplands,resulting in the formation of highly significant and significant cold spots.(2)In the central part of the study area where man-made land surface and cultivated land are concentrated,the coupling coordination between urbanization and ecosystem service is in the intermediate dislocation and mild dislocation interval;the woodland and grassland concentration areas on both sides of the study area are ecologically fragile,and the coupling coordination between the two is in the level of less than intermediate dislocation.(3)From 2000 to 2020,urbanization and the value of ecosystem services were both negatively correlated,although the correlation coefficient was low.In the central and northeastern parts,urbanization and ecosystem service exhibited patterns of high-low,high-high,and low-low clustering.Conversely,on both sides of the study area,most of the clusters showed a low-high pattern.
