Use of Skew-Normal and Skew-t Distributions for Mixture Modeling of Freeway Speed Data

Abstract

Normal, lognormal, and other forms of distribution have been used to characterize speed data. Recently, several researchers have used the normal mixture model to fit the distribution of speed. To investigate the applicability of mixture models with other types of component density, a study was done that fits 24-h speed data collected on I-35 in Texas by using skew-normal and skew-t mixture models with an algorithm of expectation maximization type. The results show that a finite mixture of skew distributions can significantly improve the goodness of fit of speed data. Compared with normal distribution, skew-normal and skew-t distributions can accommodate skewness and excess kurtosis themselves; thus the skew mixture models require fewer components than normal mixture models to capture the asymmetry and bimodality present in speed data. The results of the study indicate that a two-component skew-t mixture model is the optimal model, and this model can better account for heterogeneity in the data. The study verifies that traffic flow condition is the main cause for heterogeneity in the 24-h speed data. The research methodology can be used to analyze freeway speed data characteristics. The findings can also be used in development and validation of microscopic simulation of freeway traffic.