= Entropy power inequality
{title2=$N(X+Y)\geq N(X)+N(Y)$}
{wiki}
For independent $n$-dimensional <random vectors> with densities and finite <differential entropies>, the <entropy power inequality> states
$$
2^{2h(X+Y)/n}\geq2^{2h(X)/n}+2^{2h(Y)/n}.
$$
The sum's <differential entropy> is required to be defined; a value $+\infty$ makes the inequality immediate. Equality for finite nondegenerate densities occurs for <Gaussian distributions> with proportional <covariance matrices>.
// Target: probability-and-statistics.bigb
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