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ABSTRACT

The pattern of empirical distributions, in particular size distributions, is often best brought out by drawing a log-histogram. The Gaussian or ‘normal’ distribution furnishes a description of the empirical distribution if the log-histogram approximates to a parabola. In many cases, however, the log-histogram is far from parabolic but may be closely approximated by a hyperbola. It is therefore natural to consider those theoretical probability distributions for which the graph of the log-probability (density) function is a hyperbola. The theory and applicability of such hyperbolic distributions have been the subject of a number of recent investigations and it is the purpose of the present paper to summarize these developments, with regard to the interest they may have to sedimentologists. A precise description of the hyperbolic distributions is given and their wide applicability is indicated. Methods for fitting these distributions to data are discussed and a number of sedimentological examples are presented. Furthermore, the question of finding dynamical explanations for the occurrence of the hyperbolic shape is considered from various points of view.