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?

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    $\begingroup$ Could you explain in what problem or analysis this expression arises? $\endgroup$ – whuber May 8 '19 at 14:47

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