Regular Article: Binary Cumulants

  • Authors:

  • David C. Torney

  • Affiliations:

  • Theoretical Biology and Biophysics, Theoretical Division, Mail Stop K710, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, f1dct@lanl.govf1

  • Venue:
  • Advances in Applied Mathematics
  • Year:
  • 2000

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Abstract

The binary cumulant is defined for joint probability distributions on binary sequences of finite length. The binary cumulant is bounded, in magnitude, by unity, and is shown to vanish if there exists any bipartition of the letter positions into statistically independent blocks. Probability distributions on binary n-sequences are shown to map injectively into their binary cumulants for all subsets of the set of letter positions. An inversion algorithm is established, recovering the joint distribution from its collection of binary cumulants.