We propose a new parametric model for the modelling and estimation of event distributions for individuals in different firms. The analysis uses panel data and takes into account individual and firm effects in a non-linear model. Non-observable factors are treated as random effects. In our application, the distribution of accidents is affected by observable and non-observable factors from vehicles, drivers, and fleets of vehicles. Observable and unobservable factors are significant to explain road accidents, which means that insurance pricing should take into account all these factors. A fixed effects model is also estimated to test the consistency of the random effects model.
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