Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or h...Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or how to estimate the parameter. There are still some open problems,such as the error analysis of parameter estimation, the theoretical proof of the convergence of theiterative algorithm for maximum likelihood estimation of parameters. The Yule-Simon distributionis a heavy-tailed distribution and the parameter is usually less than 2, so the variance does notexist. This makes it difficult to give an interval estimation of the parameter. Using the compressiontransformation, this paper proposes a method of interval estimation based on the centrallimit theorem. This method can be applied to many heavy-tailed distributions. The other twoasymptotic confidence intervals of the parameter are obtained based on the maximum likelihoodand the mode method. These estimation methods are compared in simulations and applications toempirical data.展开更多
作为电力系统中的基本量测设备,电子式电压互感器(electronic voltage transformers,EVTs)的测量精度对系统的监控、控制与安全运行至关重要。为此,提出了一种基于混合深度模型和自适应窗宽概率密度估计的互感器测量误差区间预测模型。...作为电力系统中的基本量测设备,电子式电压互感器(electronic voltage transformers,EVTs)的测量精度对系统的监控、控制与安全运行至关重要。为此,提出了一种基于混合深度模型和自适应窗宽概率密度估计的互感器测量误差区间预测模型。首先,通过改进的集合经验模态分解对历史比差特征进行数据前处理。其次,提出了基于数据驱动的双向时序卷积网络、双向门控循环单元和多头注意力机制混合深度学习模型,对分解后的不同模态分量进行预测。此外,引入自适应选择最优窗宽的核密度概率估计方法,拟合预测结果构建不同置信度下的预测区间,并比较不同核函数对于预测区间的影响。通过算例分析,验证了所提模型在提高确定性预测和概率区间预测准确度方面的有效性。展开更多
针对智能交通系统中行程时间估计的不确定性量化的难题,提出一种全局-局部不确定性感知行程时间估计方法(global and local uncertainty-aware travel time estimation,GLUTTE)。首先,通过多任务学习策略建模整体路线与各局部路段的行...针对智能交通系统中行程时间估计的不确定性量化的难题,提出一种全局-局部不确定性感知行程时间估计方法(global and local uncertainty-aware travel time estimation,GLUTTE)。首先,通过多任务学习策略建模整体路线与各局部路段的行程时间关系及其不确定性。其次,采用多粒度分位数回归方法,综合考虑全局和局部特征,提供准确的置信区间估计。实验结果表明,所提方法能够有效量化不确定性,同时保证准确性并提供可靠的置信区间,从而提升结果的可用性和可信度。展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11961035)Jiangxi Provincial Natural Science Foundation(Grant No.20224BCD41001).
文摘Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or how to estimate the parameter. There are still some open problems,such as the error analysis of parameter estimation, the theoretical proof of the convergence of theiterative algorithm for maximum likelihood estimation of parameters. The Yule-Simon distributionis a heavy-tailed distribution and the parameter is usually less than 2, so the variance does notexist. This makes it difficult to give an interval estimation of the parameter. Using the compressiontransformation, this paper proposes a method of interval estimation based on the centrallimit theorem. This method can be applied to many heavy-tailed distributions. The other twoasymptotic confidence intervals of the parameter are obtained based on the maximum likelihoodand the mode method. These estimation methods are compared in simulations and applications toempirical data.
文摘作为电力系统中的基本量测设备,电子式电压互感器(electronic voltage transformers,EVTs)的测量精度对系统的监控、控制与安全运行至关重要。为此,提出了一种基于混合深度模型和自适应窗宽概率密度估计的互感器测量误差区间预测模型。首先,通过改进的集合经验模态分解对历史比差特征进行数据前处理。其次,提出了基于数据驱动的双向时序卷积网络、双向门控循环单元和多头注意力机制混合深度学习模型,对分解后的不同模态分量进行预测。此外,引入自适应选择最优窗宽的核密度概率估计方法,拟合预测结果构建不同置信度下的预测区间,并比较不同核函数对于预测区间的影响。通过算例分析,验证了所提模型在提高确定性预测和概率区间预测准确度方面的有效性。
文摘针对智能交通系统中行程时间估计的不确定性量化的难题,提出一种全局-局部不确定性感知行程时间估计方法(global and local uncertainty-aware travel time estimation,GLUTTE)。首先,通过多任务学习策略建模整体路线与各局部路段的行程时间关系及其不确定性。其次,采用多粒度分位数回归方法,综合考虑全局和局部特征,提供准确的置信区间估计。实验结果表明,所提方法能够有效量化不确定性,同时保证准确性并提供可靠的置信区间,从而提升结果的可用性和可信度。
