1980/04/01 by R. A. Bagnold, Ole E. Barndorff–Nielsen · 2 citations
Computer Science · Environmental Science · Mathematics · #Computer science #Gaussian #Geochemistry and Geologic Mapping #Geology #Geometry #Histogram #Hyperbola #Mathematics #Morphological variations and asymmetry #Probability density function #Probability distribution #Soil Geostatistics and Mapping #Statistical physics #Statistics
paper · doi:10.1111/j.1365-3091.1980.tb01170.x
openalex publication_date 1980/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15
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.