What is the difference between density and distribution?

[loom91]

Hi,

What is the difference between a density and a distribution? As in probability distribution and probability density, or energy distribution and energy density. Thanks.

Molu

 

[Hurkyl]

A distribution is a gadget that tells you how much there is over any region of space.

A density is a gadget you have to integrate in order to find out how much there is over any region of space.


Incidentally, in the probability case, we will often define the distribution in terms of a "cumulative distribution function": we use p(x) to tell how much there is over the interval (-infinity, x).

(Or maybe it's (-infinity, x]. I can't remember)

 

[loom91]

You mean the density is the exterior drivative of the distribution? Can you give an example?