I am looking for a measure of entropy over multiple random variables, each with values between 0 and 1.
Intuitively, it seems possible to talk about the expected value of information of several variables, which is entropy, but I am not sure how to go about.
I know that in the continuous case, for a single value, we should look at the differential entropy, given by $$ - \int_0^1 f(x) log(f(x)) \partial x $$ , where $ f(x) $ is the probability distribution function, which in my case is a Beta Distribution, fitted to the data.
I am fitting a Dirichlet distribution for the multiple variable case, since it is the multivariate generalization of the beta distribution.
How do we measure the entropy of such a joint probability density function?