Information theory | Probabilistic inequalities | Statistical inequalities

Entropy power inequality

In information theory, the entropy power inequality (EPI) is a result that relates to so-called "entropy power" of random variables. It shows that the entropy power of suitably well-behaved random variables is a superadditive function. The entropy power inequality was proved in 1948 by Claude Shannon in his seminal paper "A Mathematical Theory of Communication". Shannon also provided a sufficient condition for equality to hold; Stam (1959) showed that the condition is in fact necessary. (Wikipedia).

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Differential entropy | Kullback–Leibler divergence | Limiting density of discrete points | Covariance matrix | A Mathematical Theory of Communication | Random variable | If and only if | Function (mathematics) | Lp space | Claude Shannon | Probability density function | Information theory | Entropy estimation