基于L-偏度和L-峰度的行程时间可变性表征方法

Characterization of Travel Time Variability Based on L-skewness and L-kurtosis

为了定量化测度行程时间可变性右偏且长尾的实证特征,考虑实际观测中可能存在的数据样本量不足和离群值干扰问题,提出基于线性矩的L-偏度和L-峰度用于精确表征行程时间可变性。考虑到线性矩是顺序统计量期望的线性组合,给出了避免遍历所有子样本的线性矩估计方法。根据线性矩概念,探究了L-偏度和L-峰度的数学含义和其表征行程时间可变性的有效性,以及样本L-偏度和L-峰度的计算方法。理论研究发现,在表征范围和样本估计质量方面,相较于传统偏度和峰度,L-偏度和L-峰度对行程时间可变性具有更加优越的表征能力。采用深圳市车牌照识别系统的行程时间数据集进行案例分析,从无偏性、鲁棒性和有效性3个维度证明了L-偏度和L-峰度相较于传统偏度和峰度的优越性。分析结果如下:样本L-偏度和L-峰度在样本量不足时仍然是总体近似的无偏估计,而传统偏度和峰度的系统性误差较大;L-偏度和L-峰度对离群值具有鲁棒性,而传统偏度和峰度对离群值过于敏感;样本L-偏度和L-峰度对总体的估计波动小且精度高,具有良好的估计有效性;L-偏度和L-峰度分别与传统偏度和峰度有较高相关性,但又能够辨识出不同时空下行程时间可变性分布的差异。基于L-偏度和L-峰度所表征的行程时间可变性信息,出行者、规划者和管理者能够更加精准地认知不确定性的路网运行状态,从而做出更合理的行为选择和优化决策。

In order to quantify the empirical characteristics of travel time variability with right skewness and long tail when facing insufficient samples and the effects of outliers in practice, L-skewness and L-kurtosis based on linear moments(L-moments) were proposed to accurately characterize travel time variability. Considering that L-moments are linear combinations of order statistics, the method of L-moments estimation was provided to avoid traversing all subsamples. Based on L-moments, the mathematical implications of L-skewness and L-kurtosis, the validity of characterizing travel time variability by L-skewness and L-kurtosis, and the computational method of sample L-skewness and L-kurtosis were explored. Theoretically, L-skewness and L-kurtosis are superior to traditional skewness and kurtosis for characterizing travel time variability in terms of the range of characterization and the quality of estimation. Based on the realistic travel time datasets extracted from the automatic vehicle identification system in Shenzhen, China, the advantages of L-skewness and L-kurtosis over traditional skewness and kurtosis were examined from aspects of unbiasedness, robustness and validity. The results show that sample L-skewness and L-kurtosis are approximate unbiased estimators for population even with insufficient samples;however, systematic errors of traditional skewness and kurtosis are large. L-skewness and L-kurtosis are robust against outliers, while traditional skewness and kurtosis are too sensitive to outliers. Sample L-skewness and L-kurtosis have smaller variation but more accuracy in estimating than traditional skewness and kurtosis, showing the considerable validity of estimation. L-skewness and L-kurtosis are highly correlated with traditional skewness and kurtosis respectively, but they can identify the differences of travel time variability distributions on different time periods and links. According to the information of travel time variability characterized by L-skewness and L-kurtosis, travelers, planners and managers can better understand the uncertain road network, so as to make more reasonable behavioral choices and optimization decisions.