Please look at the the image of the cdf and how it rotates about a specific point:
The tricky thing is to figure out how the parameters of the distribution map to the rotation point. ANY parameter change will cause a rotation somewhere, but I want to be able to control where the rotation occurs.
I think that the underlying pdf probably can't be symmetric if you want to control the rotation point. For instance, in the case of a normal distribution, you probably have to change both the mean and the variance in a particular way to control the rotation point.
How do I control the rotation point?
I would like to use a t distribution or normal distribution. I need to control the rotation point of a pdf as well.