The location of industrial facilities is a matter of considerable public concern following recent wellpublicized disasters. In future, any development decisions must take into account the likely impact on the surrounding environment of possible accident scenarios and the risks involved. For an atmospheric release of a toxic gas, the concentration level and the duration of exposure will be critical in assessing the potential hazards. One measure proposed for determining just such an assessment is the generalized dosage D n . This paper describes a method for estimating the statistical properties of D n , based on the fact that the concentration, G, of any gas released into the atmosphere is a random variable and is fully described by its associated probability density function (pdf). Two scenarios are discussed: a comparatively long term release from a continuous source of gas, in which the pdf is assumed to be statistically stationary, and an instantaneous release in which the pdf evolves with time. The eects of varying the response time of the body exposed to the gas are investigated. The emphasis is placed on simple modelling ideas, with an eye on possible predictive schemes in the future.