Yup, that works. I would only caution that “assuming no jumps in the cdf” is not quite the right condition: singular distributions (e.g., the Cantor distribution) contain jumps, and the PIT works fine for them. The correct condition is that the random variable not have a discrete component.
Yup, that works. I would only caution that “assuming no jumps in the cdf” is not quite the right condition: singular distributions (e.g., the Cantor distribution) contain jumps, and the PIT works fine for them. The correct condition is that the random variable not have a discrete component.
Sure.