Distributional shape triangles with some applications in sedimentology

  • O. E. Barndorff-Nielsen
  • C. Christiansen
  • D. Hartmann
Part of the Acta Mechanica Supplementum book series (ACTA MECH.SUPP., volume 2)


The location-scale invariant parameters χ and ξ of the hyperbolic distribution have a triangular domain of variation which is referred to as the hyperbolic shape triangle. There are close analogies between the hyperbolic distributions, the generalized logistic distributions and the beta distributions, which make it possible also to define a logistic or a beta shape triangle.

Using a population concept of sediment samples it is shown that both the hyperbolic shape triangle and the beta shape triangle provide useful information on variations of grain size distributions, in cross-shore transects. This information can be related to the process-oriented erosion/deposition model developed previously in connection with the hyperbolic shape triangle.


Grain Size Distribution Beta Distribution Littoral Environment Invariant Parameter Swash Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • O. E. Barndorff-Nielsen
    • 1
  • C. Christiansen
    • 2
  • D. Hartmann
    • 3
  1. 1.Department of Theoretical StatisticsInstitute of MathematicsDenmark
  2. 2.Department of Earth SciencesAarhus UniversityAarhus CDenmark
  3. 3.Israel Oceanographic and Limnological Research Ltd.HaifaIsrael

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