- #1
thrillhouse86
- 80
- 0
Hey All - I am trying to solve a problem that should be really easy (at least every paper I read says the step is!)
I'm trying to understand where the Vasicek entropy estimator comes from:
I can write the differential entropy of a system as:
[tex]
H(f) = -\int^{\infty}_{-\infty} f(x)log(f(x))dx
[/tex]
where f(x) is your probability distribution function
Apparently it is an easy step that you can re-write this in the form:
[tex]
H(f) = \int^{1}_{0} log(\frac{d}{dp}F^{-1}(p)) dp
[/tex]
Where [tex] F^{1} [/tex] is the inverse of the culmative distribution function.
I've tried using the derivative of an inverse function that I learned when trying to find the derivative of inverse trig functions but all I got was:
[tex]
\frac{d F^{-1}(p)}{dp} = \frac{1}{f(F^{-1}(p))}
[/tex]
By the way just in case I need to point it out - this isn't homework - its a stupid problem which is making me feel incredibly stupid not being able to solve
Thanks,
Thrillhouse
I'm trying to understand where the Vasicek entropy estimator comes from:
I can write the differential entropy of a system as:
[tex]
H(f) = -\int^{\infty}_{-\infty} f(x)log(f(x))dx
[/tex]
where f(x) is your probability distribution function
Apparently it is an easy step that you can re-write this in the form:
[tex]
H(f) = \int^{1}_{0} log(\frac{d}{dp}F^{-1}(p)) dp
[/tex]
Where [tex] F^{1} [/tex] is the inverse of the culmative distribution function.
I've tried using the derivative of an inverse function that I learned when trying to find the derivative of inverse trig functions but all I got was:
[tex]
\frac{d F^{-1}(p)}{dp} = \frac{1}{f(F^{-1}(p))}
[/tex]
By the way just in case I need to point it out - this isn't homework - its a stupid problem which is making me feel incredibly stupid not being able to solve
Thanks,
Thrillhouse
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