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Random Sets: Models and Statistics
Author(s) -
Stoyan Dietrich
Publication year - 1998
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.1998.tb00403.x
Subject(s) - boolean model , poisson distribution , excursion , mathematics , voronoi diagram , random function , mathematical statistics , statistical physics , random field , computer science , statistics , geometry , physics , political science , law
Summary This paper surveys aspects of the theory of random closed sets, focussing on issues of practical and current interest. First, some historical remarks on this part of probability theory are made, where the important role of Georges Matheron is emphasized. Then, fundamental characteristics of the distribution of random closed sets are introduced. The very important Boolean model serves as an example for discussing mathematical and statistical problems. A number of further models is then considered, namely excursion sets of random fields, the system of edges of the Poisson Voronoi tessellation and various random systems of non‐overlapping spheres. Finally, some ideas of particle statistics are presented, including some models of random compact sets.