Reliable Computing

, Volume 11, Issue 3, pp 207–233

Exact Bounds on Finite Populations of Interval Data

  • Scott Ferson
  • Lev Ginzburg
  • Vladik Kreinovich
  • Luc Longpré
  • Monica Aviles
Article

DOI: 10.1007/s11155-005-3616-1

Cite this article as:
Ferson, S., Ginzburg, L., Kreinovich, V. et al. Reliable Comput (2005) 11: 207. doi:10.1007/s11155-005-3616-1

Abstract

In this paper, we start research into using intervals to bound the impact of bounded measurement errors on the computation of bounds on finite population parameters (“descriptive statistics”). Specifically, we provide a feasible (quadratic time) algorithm for computing the lower bound \(\underline{\sigma^2}\) on the finite population variance function of interval data. We prove that the problem of computing the upper bound \(\bar{\sigma}^2\) is, in general, NP-hard. We provide a feasible algorithm that computes \(\bar{\sigma}^2\) under reasonable easily verifiable conditions, and provide preliminary results on computing other functions of finite populations.

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Scott Ferson
    • 1
  • Lev Ginzburg
    • 1
  • Vladik Kreinovich
    • 1
  • Luc Longpré
    • 2
  • Monica Aviles
    • 2
  1. 1.Applied BiomathematicsSetauketUSA
  2. 2.Computer Science DepartmentUniversity of Texas at El PasoEl PasoUSA