Abstract
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 language | American English |
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Article number | 315 |
Pages (from-to) | 1-13 |
Journal | Entropy |
Volume | 19 |
Issue number | 7 |
DOIs | |
State | Published - 1 Jul 2017 |
Keywords
- Entropy
- Missing mass
- Probability estimate
- Sampling
All Science Journal Classification (ASJC) codes
- General Physics and Astronomy