Mathematical Geology

, Volume 28, Issue 5, pp 601–624 | Cite as

A general family of counting distributions suitable for modeling cluster phenomena

  • Jef Caers


The two-dimensional spatial distribution of precious stones, such as diamonds in alluvial and coastal deposits, shows a high degree of clustering. Usually, stones tend to gather in relatively small clusters or traps, made by potholes, gullies, or small depressions in the rough bedcock. Therefore, when taking samples of such deposits, discrete distributions of the number of stones counted in each sample yield an extreme skewness. Most samples have no stones, whereas samples containing a few hundred stones are not unusual. This paper constructs a model and a method for fitting a new and general family of counting distributions based on the Neyman-Scott cluster model and the mixed Poisson process, which can be used to model a differing degree of clustering. General recursion equations for the discrete probabilities of these distributions are derived. Application of this model to simulated data shows that information such as cluster size, number of point events per cluster, and number of clusters per measurement unit can be extracted easily from this model. Fitting the model to data of two real diamond deposits of a totally different nature—small rich clusters of Namibia versus larger but less rich clusters of Guinea—demonstrates its flexibility.

Key words

discrete distribution Neyman-Scott cluster process mixed Poisson compound Poisson discrete random function diamond deposit 


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Copyright information

© International Association for Mathematical Geology 1996

Authors and Affiliations

  • Jef Caers
    • 1
  1. 1.Department of Civil EngineeringKU LeuvenHeverleeBelgium

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