  Naturalistic driving data were applied to study driver acceleration
behaviour, and a probability model of the driver was proposed. First, the
question of whether the database is large enough is resolved using kernel
density estimation and Kullback-Liebler divergence. Next, the convergence
database is utilised to achieve the bivariate acceleration distribution
pattern. Subsequently, two probability models are proposed to explain the
pattern. Finally, the statistical characteristics of the acceleration
behaviours are studied to verify the probability models. The longitudinal and
lateral acceleration behaviours always approximate a similar Pareto
distribution. The braking, accelerating, and steering manoeuvres become more
intense at first and then less intense as the velocity increases. These
behaviours characteristics reveal the mechanism of the quadrangle bivariate
acceleration distribution pattern. The bivariate acceleration behaviour of the
driver will never reach a circle-shaped pattern. The bivariate Pareto
distribution model can be applied to describe the bivariate acceleration
behaviour of the driver.
