Definition:Differential Entropy

Definition
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.