Exponentially decreasing distributions for the logarithm of particle size

Abstract

The family of continuous type distributions such that the logarithm of the probability (density) function is a hyperbola (or, in several dimensions, a hyperboloid) is introduced and investigated. It is, among other things, shown that a distribution of this kind is a mixture of normal distributions. As to applications, the paper focuses on the mass-size distribution of aeolian sand deposits, with particular reference to the findings of R. A. Bagnold. The distribution family seems, however, to be of some potential usefulness in other concrete contexts too.