Density sum

[juliastats]

Density sum

[simonbyrne]

Good question: in general, no.

A density function of a continuous distribution should integrate to 1. However what is stored in the density array is not the function itself, but the values of the function at a set of regularly spaced points. If we double the resolution (i.e. halve the step of the range object), then this sum should double.

The long story short, the property that should hold is that for any UnivariateKDE object

sum(k.density)*step(k.x) == 1

(approximately, there will be some numeric rounding error), and for BivariateKDE objects

sum(k.density)*step(k.x)*step(k.y) == 1

(I'm going to leave this issue open to remind myself to put this in the docs when I get around to them).

[tpanum]

Thanks a ton for the clarification.