The expected missing mass under an entropy constraint

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3 Scopus citations


In Berend and Kontorovich (2012), the following problem was studied: A random sample of size t is taken from a world (i.e., probability space) of size n; bound the expected value of the probability of the set of elements not appearing in the sample (unseen mass) in terms of t and n. Here we study the same problem, where the world may be countably infinite, and the probability measure on it is restricted to have an entropy of at most h. We provide tight bounds on the maximum of the expected unseen mass, along with a characterization of the measures attaining this maximum.

Original languageEnglish
Article number315
Pages (from-to)1-13
Issue number7
StatePublished - 1 Jul 2017


  • Entropy
  • Missing mass
  • Probability estimate
  • Sampling

ASJC Scopus subject areas

  • General Physics and Astronomy


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