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

This paper documents the application of a hidden Markov model with Conway- Maxwell-Poisson(CMP) state-dependent distribution. The CMP distribution originally delevoped by Conway and Maxwell(1962) for modeling ques and service rates. And recently CMP has been re-introduced by Shmueli et al.(2005) for analyzing count data subjected to over- and under-dispersion. Over the past half centry, Hidden Markov Models(HMMs) have become increasingly popular tools for modeling time series data where, at each point in time, a hidden state process selects among a finite set of possible distributions for the observations. We model the distributions of the traffic accident covearing the period 2020, compring T=366 ovservations in total, using CMP-HMM and Poisson-HMM, which allows for overdispersion and serial dependence. Our results indicate two-state CMP-HMM is improvement on the two-state Poisson-HMM by AIC and BIC. Also we present the full array of the conditional distributions, i.e., the distribution of 𝑋ₜ conditioned on all the other observations at all times other than 𝑡.