A seminar by Associate Professor Shogo Kato from Institute of Statistical Mathematics
Title: A tractable and interpretable family of distributions on the circle, and its mixture model for traffic count data analysis
Abstract: In this talk we discuss a four-parameter family of distributions and its mixture model. The four-parameter family is a class of unimodal distributions on the circle (Kato and Jones, 2015). Some tractable properties of the family are introduced, including simple forms of density functions and trigonometric moments, clear interpretation of parameters, and a wide range of skewness and kurtosis. Then we consider mixtures of the four-parameter distributions motivated by traffic count data that are multimodal and skewed (Nagasaki et al., 2022). Identifiability holds for a reparametrized version of the mixture model under certain conditions on the parameter space. Two methods for parameter estimation, namely, a modified method of moments and the maximum likelihood method, are presented. These methods are seen to be useful for fitting the proposed mixtures to the traffic count data that show the variation of traffic volume within a day. As a result, the variation in traffic volume is classified into the morning and evening traffic whose distributions have different shapes, particularly different degrees of skewness and kurtosis.
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