This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estima...This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.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
In this article, we study the nonlinear stochastic heat equation in the spatial domain R^d subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnega...In this article, we study the nonlinear stochastic heat equation in the spatial domain R^d subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function that satisfies Dalang's condition. We establish the existence and uniqueness of a random field solution starting from measure-valued initial data. We find the upper and lower bounds for the second moment. With these moment bounds, we first establish some necessary and sufficient conditions for the phase transition of the moment Lyapunov exponents, which extends the classical results from the stochastic heat equation on Z^d to that on R^d.Then, we prove a localization result for the intermittency fronts, which extends results by Conus and Khoshnevisan [9] from one space dimension to higher space dimension. The linear case has been recently proved by Huang et al [17] using different techniques.展开更多
In this paper, we propose a new method that combines collage error in fractal domain and Hu moment invariants for image retrieval with a statistical method - variable bandwidth Kernel Density Estimation (KDE). The pro...In this paper, we propose a new method that combines collage error in fractal domain and Hu moment invariants for image retrieval with a statistical method - variable bandwidth Kernel Density Estimation (KDE). The proposed method is called CHK (KDE of Collage error and Hu moment) and it is tested on the Vistex texture database with 640 natural images. Experimental results show that the Average Retrieval Rate (ARR) can reach into 78.18%, which demonstrates that the proposed method performs better than the one with parameters respectively as well as the commonly used histogram method both on retrieval rate and retrieval time.展开更多
We develop higher order accurate estimators of integrated volatility in a stochastic volatility models by using kernel smoothing method and using different weights to kernels. The weights have some relationship to mom...We develop higher order accurate estimators of integrated volatility in a stochastic volatility models by using kernel smoothing method and using different weights to kernels. The weights have some relationship to moment problem. As the bandwidth of the kernel vanishes, an estimator of the instantaneous stochastic volatility is obtained. We also develop some new estimators based on smoothing splines.展开更多
Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed...Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.展开更多
In this paper, we derive a new method for estimating the parameters of the K-distribution when a limited number of samples are available. The method is based on an approximation of the Bessel function of the second ki...In this paper, we derive a new method for estimating the parameters of the K-distribution when a limited number of samples are available. The method is based on an approximation of the Bessel function of the second kind that reduces the complexity of the estimation formulas in comparison to those used by the maximum likelihood algorithm. The proposed method has better performance in comparison with existing methods of the same complexity giving a lower mean squared error when the number of samples used for the estimation is relatively low.展开更多
针对爆炸用激波管缺乏相应的经验公式和数值模拟时效性差的问题,同时为了快速得到激波管内的峰值压力,建立预测爆炸用激波管试验段峰值压力的四层反向传播(back propagation,BP)神经网络。采用数值模拟方法计算激波管试验段峰值压力,计...针对爆炸用激波管缺乏相应的经验公式和数值模拟时效性差的问题,同时为了快速得到激波管内的峰值压力,建立预测爆炸用激波管试验段峰值压力的四层反向传播(back propagation,BP)神经网络。采用数值模拟方法计算激波管试验段峰值压力,计算结果与激波管爆炸试验结果进行对比,平均相对误差为2.69%。证明激波管数值模型的准确性后,将数值模拟得到的195组激波管测得的峰值压力作为输出层,激波管驱动段TNT的药量、药柱的长径比以及爆炸比例距离作为神经网络的输入层。为了加快神经网络迭代速度和提高预测精度,使用自适应矩估计(adaptive moment estimation,ADAM)算法作为神经网络误差梯度下降的优化算法。结果表明,训练好的神经网络得到的预测结果与模拟值基本吻合,预测结果与数值模拟结果的平均相对误差为3.26%。BP神经网络模型能够反映激波管爆炸的峰值压力与影响因素之间的映射关系,采用BP神经网络模型计算时比数值模拟节约了大量运算时间。展开更多
This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation ...This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.展开更多
文摘This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.
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supported by the National Research Foundation of Korea (NRF-2017R1C1B1005436)the TJ Park Science Fellowship of POSCO TJ Park Foundation
文摘In this article, we study the nonlinear stochastic heat equation in the spatial domain R^d subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function that satisfies Dalang's condition. We establish the existence and uniqueness of a random field solution starting from measure-valued initial data. We find the upper and lower bounds for the second moment. With these moment bounds, we first establish some necessary and sufficient conditions for the phase transition of the moment Lyapunov exponents, which extends the classical results from the stochastic heat equation on Z^d to that on R^d.Then, we prove a localization result for the intermittency fronts, which extends results by Conus and Khoshnevisan [9] from one space dimension to higher space dimension. The linear case has been recently proved by Huang et al [17] using different techniques.
基金Supported by the Fundamental Research Funds for the Central Universities (No. NS2012093)
文摘In this paper, we propose a new method that combines collage error in fractal domain and Hu moment invariants for image retrieval with a statistical method - variable bandwidth Kernel Density Estimation (KDE). The proposed method is called CHK (KDE of Collage error and Hu moment) and it is tested on the Vistex texture database with 640 natural images. Experimental results show that the Average Retrieval Rate (ARR) can reach into 78.18%, which demonstrates that the proposed method performs better than the one with parameters respectively as well as the commonly used histogram method both on retrieval rate and retrieval time.
文摘We develop higher order accurate estimators of integrated volatility in a stochastic volatility models by using kernel smoothing method and using different weights to kernels. The weights have some relationship to moment problem. As the bandwidth of the kernel vanishes, an estimator of the instantaneous stochastic volatility is obtained. We also develop some new estimators based on smoothing splines.
文摘Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.
文摘In this paper, we derive a new method for estimating the parameters of the K-distribution when a limited number of samples are available. The method is based on an approximation of the Bessel function of the second kind that reduces the complexity of the estimation formulas in comparison to those used by the maximum likelihood algorithm. The proposed method has better performance in comparison with existing methods of the same complexity giving a lower mean squared error when the number of samples used for the estimation is relatively low.
文摘针对爆炸用激波管缺乏相应的经验公式和数值模拟时效性差的问题,同时为了快速得到激波管内的峰值压力,建立预测爆炸用激波管试验段峰值压力的四层反向传播(back propagation,BP)神经网络。采用数值模拟方法计算激波管试验段峰值压力,计算结果与激波管爆炸试验结果进行对比,平均相对误差为2.69%。证明激波管数值模型的准确性后,将数值模拟得到的195组激波管测得的峰值压力作为输出层,激波管驱动段TNT的药量、药柱的长径比以及爆炸比例距离作为神经网络的输入层。为了加快神经网络迭代速度和提高预测精度,使用自适应矩估计(adaptive moment estimation,ADAM)算法作为神经网络误差梯度下降的优化算法。结果表明,训练好的神经网络得到的预测结果与模拟值基本吻合,预测结果与数值模拟结果的平均相对误差为3.26%。BP神经网络模型能够反映激波管爆炸的峰值压力与影响因素之间的映射关系,采用BP神经网络模型计算时比数值模拟节约了大量运算时间。
基金This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(Grant Number IMSIU-RG23142).
文摘This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.
