Hypothesis testing in integral geometry

Author:
Peter Waksman

Journal:
Trans. Amer. Math. Soc. **296** (1986), 507-520

MSC:
Primary 60D05; Secondary 52A22

DOI:
https://doi.org/10.1090/S0002-9947-1986-0846595-2

MathSciNet review:
846595

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Abstract: Probability distributions are defined relative to a fixed plane domain and are calculated explicitly when the domain is a union of coordinate rectangles. The theory of approximating step functions by the resulting special functions gives an interpretation of the problem of guessing a domain given a random sample of observations.

**[1]**Thomas S. Ferguson,*Mathematical statistics: A decision theoretic approach*, Probability and Mathematical Statistics, Vol. 1, Academic Press, New York-London, 1967. MR**0215390****[2]**William F. Pohl,*The probability of linking of random closed curves*, Lecture Notes in Math., vol. 894, Springer, Berlin-New York, 1981, pp. 113–126. MR**655422****[3]**G. Polya,*Patterns of plausible inference*, Princeton Univ. Press, Princeton, N. J., 1954, p. 84.**[4]**Luis A. Santaló,*Integral geometry and geometric probability*, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. With a foreword by Mark Kac; Encyclopedia of Mathematics and its Applications, Vol. 1. MR**0433364****[5]**P. Waksman,*The associated function of a plane polygon*, Ph.D. Dissertation, Univ. of Minnesota, 1983.**[6]**-,*Plane polygons and a conjecture of Blaschke's*, J. Appl. Probab. (to appear).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0846595-2

Keywords:
Guessing shape,
random lines,
statistics

Article copyright:
© Copyright 1986
American Mathematical Society