# Name/definition of $\int \log F(x) \cdot g(x)dx$?

We know that:

$$-\int \log f(x) \cdot g(x)dx,$$ where $$f$$ and $$g$$ are density functions, is known as the cross entropy. Does $$-\int \log F(x) \cdot g(x)dx,$$ where $$F$$ is the cumulative distribution function of $$f$$, have a name?

• Could you explain in what problem or analysis this expression arises? – whuber May 8 at 14:47