Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T14:17:50.696Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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