Good and Bad Drivers - A Markov Model of Accident Proneness

Existing models of the distribution of accidents among a population of drivers do not account for both the differences among individuals and those among age groups. This paper proposes a simple model to simultaneously explain these variations. The model assumes that all drivers begin at some early age as “bad” drivers. Subsequently, drivers switch at random from the “bad” state, with high accident probabilities per mile driven, to a “good” state with low accident probabilities. The opposite transition, from “good” to “bad” states, also occurs at random. As the proportion of good drivers increases with age, the average frequency declines with age. The author develops in his paper the explicit mathematical equations of the model and a method of parameter estimation.