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Estimators for distances

Published online by Cambridge University Press:  14 July 2016

E. N. Gilbert
E. N. Gilbert*
Affiliation:
Bell Laboratories, Murray Hill, New Jersey
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Abstract

This paper compares estimators of u = |P2 — P1| based on partial knowledge about points P1, P2 which are chosen independently from the same probability distribution in the plane. Typical estimators are the conditional expectations E(u | r1, r2), E(u | s), E(u | rM), E(u | θ) where ri is the distance from Pi to the origin 0, s = r1 + r2, rM = Max{r1, r2}, θ = ∠ P10P2. These expectations are the least squares estimators, given the conditioned variables. Simpler linear estimators are also considered.

Keywords

BILLINGGEOMETRIC PROBABILITYESTIMATIONMEAN LENGTHPRICINGNETWORKPLANERANDOM POINTSTELEPHONY
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 260 - 271
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] Uspensky, J. V. (1937) Introduction to Mathematical Probability. McGraw-Hill, New York.Google Scholar
[2] Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. 2. McGraw-Hill, New York.Google Scholar