Applications of the Conway-Maxwell-Poisson Hidden Markov models for analyzing traffic accident

Abstract

This paper documents the application of the Conway-Maxwell-Poisson(CMP) hidden Markov model for modelling motor vehicle crashes. The CMP distribution is a twoparameter extension of the Poisson distribution that generalizes some well-known discrete distributions(Poisson, Bernoulli and geometric). Also it leads to the generalizations of distributions derived from theses discrete distributions, that is, the binomial and negative binomial distributions. The advantage of CMP distribution is its ability to handle both under and over-dispersion through controlling one special parameter in the distribution, which makes it more flexible than Poisson distribution. We consider the data consisting of the daily number of injuries on the road in 2020 from the TAAS(Traffic Accident Analysis System). We apply CMP hidden Markov model to data, the parameters are estimated via maximim likelihood, and find that this model achieves better performance than commonly used Poisson hidden Markov model. For the decoding procedure, the Viterbi algorithm is implemented.