We prove that non-recursive base conversion can always be implemented by using a deterministic Markov process. Our paper discusses the pros and cons of recursive and non-recursive methods, in general. And we include a...We prove that non-recursive base conversion can always be implemented by using a deterministic Markov process. Our paper discusses the pros and cons of recursive and non-recursive methods, in general. And we include a comparison between non-recursion and a deterministic Markov process, proving that the Markov process is twice as efficient.展开更多
Reducing the input wind and photovoltaic power time series data can improve the efficiency of time sequential simulations.In this paper,a wind and photovoltaic power time series data aggregation method based on an ens...Reducing the input wind and photovoltaic power time series data can improve the efficiency of time sequential simulations.In this paper,a wind and photovoltaic power time series data aggregation method based on an ensemble clustering and Markov chain(ECMC)is proposed.The ECMC method can effectively reduce redundant information in the data.First,the wind and photovoltaic power time series data were divided into scenarios,and ensemble clustering was used to cluster the divided scenarios.At the same time,the Davies-Bouldin Index(DBI)is adopted to select the optimal number of clusters.Then,according to the temporal correlation between wind and photovoltaic scenarios,the wind and photovoltaic clustering results are merged and reduced to form a set of combined typical day scenarios that can reflect the characteristics of historical data within the calculation period.Finally,based on the Markov Chain,the state transition probability matrix of various combined typical day scenarios is constructed,and the aggregation state sequence of random length is generated,and then,the combined typical day scenarios of wind and photovoltaic were sampled in a sequential one-way sequence according to the state sequence and then are built into a representative wind and photovoltaic power time series aggregation sequence.A provincial power grid was chosen as an example to compare the multiple evaluation indexes of different aggregation methods.The results show that the ECMC aggregation method improves the accuracy and efficiency of time sequential simulations.展开更多
Let (■_n)≥0 be the Markov chain of two states with respect to the probability measure of the maximal entropy on the subshift spaceΣ_A defined by Fibonacci incident matrix A.We consider the measureμ_λof the probab...Let (■_n)≥0 be the Markov chain of two states with respect to the probability measure of the maximal entropy on the subshift spaceΣ_A defined by Fibonacci incident matrix A.We consider the measureμ_λof the probability distribution of the random seriesΣ_(n=0)~∞■_nλ~n(0<λ<1).It is proved thatμ_λis singular ifλ∈(0,(5^(1/2)-1)/2) and thatμ_λis absolutely continuous for almost allλ∈((5^(1/2)-1)/2,0.739).展开更多
Numerous methodologies have been developed in the literature for the generation of rain. However, in semi-arid areas where the irregularity of rain is contrasted, the question of the applicability of these models is s...Numerous methodologies have been developed in the literature for the generation of rain. However, in semi-arid areas where the irregularity of rain is contrasted, the question of the applicability of these models is still relevant. The objective of this article is to propose a development method of stochastic generator of monthly rainfall series. The present work is based on the modeling of the occurrence and the quantity of rain in a separate way. The occurrence is treated in two stages. The first step considers the Markov chain according to the occurrence of annual statements (dry, average and wet). The second step uses the monthly rankings. The amount of rain is calculated based on historical series according to the monthly rank and the annual statement noted. This method is applied to rainfall data recorded at five rainfall stations in semi-arid region of Central Tunisia. The usual and conventional statistical tests of the generated series have shown the validity of this method.展开更多
Stochastic weather generators are statistical models that produce random numbers that resemble the observed weather data on which they have been fitted; they are widely used in meteorological and hydrologi- cal simula...Stochastic weather generators are statistical models that produce random numbers that resemble the observed weather data on which they have been fitted; they are widely used in meteorological and hydrologi- cal simulations. For modeling daily precipitation in weather generators, first-order Markov chain–dependent exponential, gamma, mixed-exponential, and lognormal distributions can be used. To examine the perfor- mance of these four distributions for precipitation simulation, they were fitted to observed data collected at 10 stations in the watershed of Yishu River. The parameters of these models were estimated using a maximum-likelihood technique performed using genetic algorithms. Parameters for each calendar month and the Fourier series describing parameters for the whole year were estimated separately. Bayesian infor- mation criterion, simulated monthly mean, maximum daily value, and variance were tested and compared to evaluate the fitness and performance of these models. The results indicate that the lognormal and mixed-exponential distributions give smaller BICs, but their stochastic simulations have overestimation and underestimation respectively, while the gamma and exponential distributions give larger BICs, but their stochastic simulations produced monthly mean precipitation very well. When these distributions were fitted using Fourier series, they all underestimated the above statistics for the months of June, July and August.展开更多
Nonparametric stochastic volatility models,although providing great flexibility for modelling thevolatility equation,often fail to account for useful shape information.For example,a model maynot use the knowledge that...Nonparametric stochastic volatility models,although providing great flexibility for modelling thevolatility equation,often fail to account for useful shape information.For example,a model maynot use the knowledge that the autoregressive component of the volatility equation is monotonically increasing as the lagged volatility increases.We propose a class of additive stochasticvolatility models that allow for different shape constraints and can incorporate the leverageeffect–asymmetric impact of positive and negative return shocks on volatilities.We developa Bayesian fitting algorithm and demonstrate model performance on simulated and empiricaldatasets.Unlike general nonparametric models,our model sacrifices little when the true volatility equation is linear.In nonlinear situations we improve the model fit and the ability to estimatevolatilities over general,unconstrained,nonparametric models.展开更多
文摘We prove that non-recursive base conversion can always be implemented by using a deterministic Markov process. Our paper discusses the pros and cons of recursive and non-recursive methods, in general. And we include a comparison between non-recursion and a deterministic Markov process, proving that the Markov process is twice as efficient.
基金supported by the National Key R&D Program of China(2017YFB0902200)Science and Technology Project of State Grid Corporation of China(4000-202255057A-1-1-ZN,5228001700CW).
文摘Reducing the input wind and photovoltaic power time series data can improve the efficiency of time sequential simulations.In this paper,a wind and photovoltaic power time series data aggregation method based on an ensemble clustering and Markov chain(ECMC)is proposed.The ECMC method can effectively reduce redundant information in the data.First,the wind and photovoltaic power time series data were divided into scenarios,and ensemble clustering was used to cluster the divided scenarios.At the same time,the Davies-Bouldin Index(DBI)is adopted to select the optimal number of clusters.Then,according to the temporal correlation between wind and photovoltaic scenarios,the wind and photovoltaic clustering results are merged and reduced to form a set of combined typical day scenarios that can reflect the characteristics of historical data within the calculation period.Finally,based on the Markov Chain,the state transition probability matrix of various combined typical day scenarios is constructed,and the aggregation state sequence of random length is generated,and then,the combined typical day scenarios of wind and photovoltaic were sampled in a sequential one-way sequence according to the state sequence and then are built into a representative wind and photovoltaic power time series aggregation sequence.A provincial power grid was chosen as an example to compare the multiple evaluation indexes of different aggregation methods.The results show that the ECMC aggregation method improves the accuracy and efficiency of time sequential simulations.
文摘Let (■_n)≥0 be the Markov chain of two states with respect to the probability measure of the maximal entropy on the subshift spaceΣ_A defined by Fibonacci incident matrix A.We consider the measureμ_λof the probability distribution of the random seriesΣ_(n=0)~∞■_nλ~n(0<λ<1).It is proved thatμ_λis singular ifλ∈(0,(5^(1/2)-1)/2) and thatμ_λis absolutely continuous for almost allλ∈((5^(1/2)-1)/2,0.739).
文摘Numerous methodologies have been developed in the literature for the generation of rain. However, in semi-arid areas where the irregularity of rain is contrasted, the question of the applicability of these models is still relevant. The objective of this article is to propose a development method of stochastic generator of monthly rainfall series. The present work is based on the modeling of the occurrence and the quantity of rain in a separate way. The occurrence is treated in two stages. The first step considers the Markov chain according to the occurrence of annual statements (dry, average and wet). The second step uses the monthly rankings. The amount of rain is calculated based on historical series according to the monthly rank and the annual statement noted. This method is applied to rainfall data recorded at five rainfall stations in semi-arid region of Central Tunisia. The usual and conventional statistical tests of the generated series have shown the validity of this method.
基金supported by the National Key Developing Program for Basic Sciences of China (GrantNo. 2010CB951404)Chinese Nature Science Foundation(Grant No. 40971024)the Special Meteorology Project[GYHY(QX)2007-6-1]
文摘Stochastic weather generators are statistical models that produce random numbers that resemble the observed weather data on which they have been fitted; they are widely used in meteorological and hydrologi- cal simulations. For modeling daily precipitation in weather generators, first-order Markov chain–dependent exponential, gamma, mixed-exponential, and lognormal distributions can be used. To examine the perfor- mance of these four distributions for precipitation simulation, they were fitted to observed data collected at 10 stations in the watershed of Yishu River. The parameters of these models were estimated using a maximum-likelihood technique performed using genetic algorithms. Parameters for each calendar month and the Fourier series describing parameters for the whole year were estimated separately. Bayesian infor- mation criterion, simulated monthly mean, maximum daily value, and variance were tested and compared to evaluate the fitness and performance of these models. The results indicate that the lognormal and mixed-exponential distributions give smaller BICs, but their stochastic simulations have overestimation and underestimation respectively, while the gamma and exponential distributions give larger BICs, but their stochastic simulations produced monthly mean precipitation very well. When these distributions were fitted using Fourier series, they all underestimated the above statistics for the months of June, July and August.
基金Peter Craigmile and Jiangyong Yin were supported in part by the National Science Foundation(NSF)under grant DMS-0906864Xinyi Xu,Jiangyong Yin and Steven MacEachern were supported in part by the NSF under grant DMS-1209194+2 种基金Peter Craigmile is additionally supported in part by the NSF under grants SES-1024709,DMS-1407604 and SES-1424481the National Cancer Institute of the National Institutes of Health under Award Number 1R21CA212308-01the project title is‘Evaluating how licensing-law strategies will change neighborhood disparities in tobacco retailer density’.Xinyi Xu and Steven MacEachern are supported under grant DMS-1613110.
文摘Nonparametric stochastic volatility models,although providing great flexibility for modelling thevolatility equation,often fail to account for useful shape information.For example,a model maynot use the knowledge that the autoregressive component of the volatility equation is monotonically increasing as the lagged volatility increases.We propose a class of additive stochasticvolatility models that allow for different shape constraints and can incorporate the leverageeffect–asymmetric impact of positive and negative return shocks on volatilities.We developa Bayesian fitting algorithm and demonstrate model performance on simulated and empiricaldatasets.Unlike general nonparametric models,our model sacrifices little when the true volatility equation is linear.In nonlinear situations we improve the model fit and the ability to estimatevolatilities over general,unconstrained,nonparametric models.
