In statistics, a distribution is random or stochastic or realised by chance, when its composing elements may occur at any moment in time or may appear in any location with some probability. A random distribution may however follow a characteristic process that gives it a particular form (e.g. Poisson distribution, normal distribution, law of Galton-Gibrat). Tables of random numbers are used in order to generate such distributions, which serve as references for comparison with observed distributions, or which allow to take samples from a population (in order to carry out a survey), or else which are used in simulation models.
In geography, chance is invoked to give account of geographical locations or distributions that do not seem explainable by any known general factor, that have an accidental character with respect to usual determining factors. Such a conclusion is generally provisional (with regard to a state of knowledge), and relative to an observation level: a distribution may appear as random at regional scale (e.g. a set of steel plants randomly established on the territory of a department), whereas at a smaller scale each of these locations may be explained by local conditions (site of mining resources). Diversity of initial situations and of local causalities in speed and forms of adaptation to change is mentioned to explain analogies that may be made, at macro-geographical scales, with random processes, in genesis and evolution of regional configurations (growth of cities, spatial diffusion of innovations).