The Entropy of a Discrete Real Variable

نویسنده

  • Scott Funkhouser
چکیده

The discrete Shannon entropy H was formulated only to measure indeterminacy effected through a set of probabilities, but the indeterminacy in a real-valued discrete variable depends on both the allowed outcomes x and the corresponding probabilities p. A fundamental measure that is sensitive to both x and p is derived here from the total differential entropy of a continuous real variable and its conjugate in the discrete limit, where the conjugate is universally eliminated. The asymptotic differential entropy recovers H plus the new measure, named Ξ, which provides a novel probe of intrinsic organization in sequences of real numbers.

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عنوان ژورنال:
  • Entropy

دوره 14  شماره 

صفحات  -

تاریخ انتشار 2012