I'm trying to create a PDF that has the max values at its tails, and a P(x) of 0 at its mean.
Essentially it would be something like two normal distributions lined up side to side.
Is there any literature regarding such a distribution? I'm trying to model the probability of exiting a position. If the price of the position doesn't move, it has the lowest probability of being exited, but the probability of exit is highest with an extreme move in either direction.