I have a time-series that appears to decay supra-exponentially. 
results in better fitness to a straight line. After taking $\log(\log(\log(y)))$, I have a great fit. This time series represents the probability over time that an event occurs (e.g., a player will continue a conversation). I need to find a function that can approximate this behavior so that I can attempt to simulate interactions. How may I go about doing this?
Thanks in advance.