Inverse Gaussian k-distributions

k-distributions corresponding to Malkmus' narrow band model are inverse Gaussian distributions. Inverse Gaussian theory developments are therefore directly relevant to gas radiative transfer modeling. The present text illustrates some significant benefits that could be made from this observation: (i) k-distribution formulations are simplified, (ii) numerical integration procedures can be optimized for each new configuration type, and (iii) frequently encountered integrals can be solved analytically and numerical integrations can be avoided. This last point is illustrated with the computation of infra-red cooling rates in planetary atmospheres.