This study investigates the possibilities for analysing accident data independently of the choice of the length of the intervals used, and consequently independently of the choice of the starting point of the sequence of accident counts. This seems to be possible using the original points of time as recorded. Techniques developed are based on the Doob-Meyer decomposition of the stochastic process of the count of accidents. It is found that many techniques are readily available. It is assumed that the accident process has an intensity process. It is found that this intensity function exists under certain regularity conditions. It is attempted to build a model based on an exponential variant of a Fourier system that estimates the intensity function. Some extensions, covering exogenous variables and intervention analysis are discussed. Some simulations and a real life problem are given. It is found that the current implementation suffers from a non-optimal goodness-of-fit criterion. It is also found that the implementation lacks the ability of inclusion of exogenous variables. The Fourier system may be extended, possibly by wavelets.
Samenvatting