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On computing the dispersion function

Abstract

A two-dimensional analogue of the well-known bisection method for root finding is presented in order to solve the following problem, related to the dispersion function of a set of random variables: given distribution functionsF 1,...,F n and a probabilityp, find an interval [a,b] of minimum width such thatF i(b)−F i(a )⩾p, fori=1,...,n.

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Additional information

The author wishes to thank Dr. I. D. Coope, for helpful advice offered during the preparation of this paper, and the referee, whose comments contributed to a clearer presentation.

Communicated by F. Zirilli

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Wood, G.R. On computing the dispersion function. J Optim Theory Appl 58, 331–350 (1988). https://doi.org/10.1007/BF00939689

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Key Words

  • Distribution function
  • dispersion function
  • concentration function
  • bisection
  • interval minimization