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collision entropy

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Definition

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The collision entropy of a probability distribution on a finite set is the Rényi entropy at order 2:

S 2(p)=log( i=1 np i 2), S_2(p) \;=\; -\log \left( \sum_{i=1}^n p_i^2 \right) \,,

hence is the negative logarithm of the “collision probability”, i.e., of the probability that two independent random variables, both described by pp, will take the same value.

order0\phantom{\to} 01\to 12\phantom{\to}2\to \infty
Rényi entropyHartley entropy\geqShannon entropy\geqcollision entropy\geqmin-entropy

References

  • G. M. Bosyk, M. Portesi, A. Plastino, Collision entropy and optimal uncertainty, Phys. Rev. A 85 (2012) 012108 (arXiv:1112.5903)

See also:

Created on May 28, 2021 at 07:33:59. See the history of this page for a list of all contributions to it.