Definition:Differential Entropy

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Differential entropy extends the concept of entropy to continuous random variables.

Let $X$ be a continuous random variable.

Let $X$ have probability density function $f_X$.

Then the differential entropy of $X$, $\map h X$ measured in nats, is given by:

$\ds \map h X = -\int_{-\infty}^\infty \map {f_X} x \ln \map {f_X} x \rd x$

Where $\map {f_X} x = 0$, we take $\map {f_X} x \ln \map {f_X} x = 0$ by convention.

Also see

  • Results about differential entropy can be found here.