The theoretical foundations of the exponential and power-law analytical formulations for the size-frequency and intensity-frequency distributions of the convective vortices, including dust devils, are re-examined. Jaynes' general statistical arguments based on Shannon's entropy maximum principle leading to an exponential distribution are supplemented by Renyi'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 moment of the distribution. Applications to statistics of convective vortices, including dust devils, on Earth and Mars are discussed. The existence of a finite expectation value of the vortex diameter related to the absolute value of the Obukhov length scale in the atmospheric boundary layer allows a quantitative explanation of a burst of convective vortex activity observed at the InSight landing site in northern autumn on Mars.
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