Probability Model of Traction Load Using Histogram Density Estimator Based on Optimal Binwidth
Yulong Che, Xiaoqin Lv, Xiaoru Wang, ZhenLi Lin, Yulong Che, Kun Jiang · 2018
Histogram is one widely used nonparametric estimation method. The shape of histogram probability density is affected by the width of bins. The measured data of traction load feeder currents and power factor have many spikes due to its fluctuation and impact. After trying a few times to change the bin size by the general rule of thumb, the appropriate probability density of traction loads can be obtained. This is laborious and without theoretical basis. This paper proposes the cost function of mean integrated squared error (MISE) to find the optimal binwidth. This method is used to establish the probability density histogram for traction load feeder currents and power factor. The probability modelling for traction load feeder currents and power factor based on histogram density estimator using optimal binwidth is labor-saving and more suitable. The best histogram obtained by this method has mathematical support when other parameter or nonparameter estimation methods are compared with the histogram.