Abstract
The Buffon needle problem and some variations are used to illustrate classical statistical methods of estimation and to lead into, and contrast with, the problems which arise when a sample of some random structure is the data. The flavor of these problems is conveyed largely by discussion of the simplest, and most described, case, that of point processes.
This technical report was originally delivered as a lecture at the button bicentenary Symposium on Geometrical probability, Image Analysis, Mathematical Stereology and their relevance to the determination of Biological Structure, Paris, June 20–24, 1977.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bartlett, M. S. (1963). The spectial analysis of point piocesses. J. Roy. Stat. Soc. B, 25, 264–296.
Bartlett, M. S. (1964). The spectial analysis of two-dimensional point piocesses. Biometrika, 51, 299–311.
Bartlett, M. S. (1976) The Statistical Analysis of Spatial pattein. Chapman & Hall, London.
Cox, A. R. & Lewis, P. A. M. (1966). The Statistical Analysis of Senies of Events. Methuen, London.
Diaconis P. (1976). Unpublished.
Grenander, U. (1976). PatteinSynthesis: Lectuies in Pattein Theory, Volume, 1. Springer-Verlag, New York.
Harding, E. F. & Kendall, D. G. (1974). Stochastic Geometiy. John Wiley & Sons, New York.
Hartman, P. & Watson, G. S. (1974). “Noimal” distributions on spheies and the moditied Bessel tunction. Ann. Prob., 2, No.4, 593–607.
Kendall, D. G. (1974). Hunting quanta. Phil. Trans. Roy. Soc. London, A, 276, 231–266.
Kendall, M. G. & Moran, A. P. (1963). Geometrical Piobability. Griffin, London.
Krickeberg, K. (1977). “STATISTICAL PROBLEMS ON POINT PROCESSES”. Conférences au Centre Banach, Varsovie, Sept. 1976.
Lallerini, M. (1901). Periodico di Mathematica, 4, 140.
Matern, B. (1960). Spatial variation. Meddelanden fran Statens Skogsforskringsinstitut, 45, No. 5.
Matheron, G. (1967). Eléments poun une theorie des milieux poieux. Masson et Cie., Paris.
Perlman, M. D. & Wichura, M. J. (1975). Shanpening button’s needle. The Amer. Stat., 29, No. 4, 157–163.
Ripley, B. D. (1977a). Modelling spatial patteins. To appear in J. Roy. Stat. Soc. A.
Ripley, B. D. (1977b). Spectial analysis and the analysis of pattein. Unpublished.
Upsensky, J. V. (1937). Intioduction to Mathematical Piobability. McGraw-Hill, New York and London.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Watson, G.S. (1978). Characteristic Statistical Problems of Stochastic Geometry. In: Miles, R.E., Serra, J. (eds) Geometrical Probability and Biological Structures: Buffon’s 200th Anniversary. Lecture Notes in Biomathematics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93089-8_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-93089-8_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08856-1
Online ISBN: 978-3-642-93089-8
eBook Packages: Springer Book Archive