Expectation and variance of the volume covered by a large number of independent random sets

A. J. Stam

Compositio Mathematica (1984)

  • Volume: 52, Issue: 1, page 57-83
  • ISSN: 0010-437X

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Stam, A. J.. "Expectation and variance of the volume covered by a large number of independent random sets." Compositio Mathematica 52.1 (1984): 57-83. <http://eudml.org/doc/89653>.

@article{Stam1984,
author = {Stam, A. J.},
journal = {Compositio Mathematica},
keywords = {random sets; random covering; asymptotic expansion},
language = {eng},
number = {1},
pages = {57-83},
publisher = {Martinus Nijhoff Publishers},
title = {Expectation and variance of the volume covered by a large number of independent random sets},
url = {http://eudml.org/doc/89653},
volume = {52},
year = {1984},
}

TY - JOUR
AU - Stam, A. J.
TI - Expectation and variance of the volume covered by a large number of independent random sets
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 52
IS - 1
SP - 57
EP - 83
LA - eng
KW - random sets; random covering; asymptotic expansion
UR - http://eudml.org/doc/89653
ER -

References

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  1. [1] L. De Haan: On regular variation and its application to the weak convergence of sample extremes. Mathematical Centre Tracts32. Amsterdam: Mathematisch Centrum, 1970. Zbl0226.60039MR286156
  2. [2] M.P. D: Differential Geometry of Curves and Surfaces. Englewood Cliffs, New Jersey: Prentice Hall, 1976. Zbl0326.53001MR394451
  3. [3] W. Feller: An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. New York: Wiley, 1971. Zbl0039.13201MR270403
  4. [4] W. Gröbner and N. Hofreiter: Integral-Tafel, Zweiter Teil: bestimmte Integrale. Wien1950. 
  5. [5] H. Hadwiger: Altes und Neues über konvexe Körper. Basel und Stuttgart: Birkhäuser Verlag, 1955. Zbl0064.16503MR73220
  6. [6] P.A.P. Moran: The volume occupied by normally distributed spheres. Acta Math.133 (1974) 273-286. Zbl0297.60011MR410844
  7. [7] E. Seneta: Regularly Varying Functions.Lecture Notes in Mathematics508. Berlin: Springer Verlag, 1976. Zbl0324.26002MR453936
  8. [8] A.J. Stam: The variance of the volume covered by a large number of rectangles with normally distributed centers. Report T. W.218, Mathematisch Instituut Rijksuniversiteit Groningen. 
  9. [9] A.J. Stam: The volume covered by a large number of random sets: examples. Report T. W.-245, Mathematisch Instituut Rijksuniversiteit, Groningen. Zbl0546.60015
  10. [10] F.A. Valentine: Konvexe Mengen. Mannheim: Bibliographisches Institut, 1968. Zbl0157.52501MR226495

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