Discrete approximations to continuous density functions that are L1 optimal

  • Authors:

  • Darryl Katz

  • Affiliations:

  • Department of Mathematics, California State University, Fullerton, CA 92634, USA

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 1983

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Abstract

An algorithm is developed for finding the L"1 optimal discrete approximation to a continuous density function, @?(x), on a closed interval for any given number, n, of points at which density is to be placed. The method requires only one dimensional optimization for any n and, hence, is computationally feasible. It is applied to two examples, one in which @?(x) is known analytically and one in which it is known only at a 'large' number of discrete points. Alternative implementations and applications are discussed.