Аннотация:The theoretical foundations of the exponential and power-law analytical formulations forthe size–frequency and intensity–frequency distributions of the convective vortices, including dust devils, are re-examined. Jaynes’ general statistical arguments based on Shannon’sentropy maximum principle leading to an exponential distribution are supplemented byRényi’s maximum entropy principle which is shown to lead to a power-law distribution.In both cases, a key ingredient of the theory is the a priori knowledge of a first finite momentof the distribution. Applications to statistics of convective vortices, including dust devils, onEarth and Mars are discussed. The existence of a finite expectation value of the vortex diameterrelated to the absolute value of the Obukhov length scale in the atmospheric boundarylayer allows a quantitative explanation of a burst of convective vortex activity observed atthe InSight landing site in northern autumn on Mars.