Use Histogram data to generate random samples in scipy
You can also use the histogram, piecewise uniform distribution directly, then you get exactly the corresponding random numbers instead of an approximation. 
The inverse cdf, ppf, is piecewise linear and linear interpolation can be used to transform uniform random numbers appropriately.
Suppose I have a process where I push a button, and after a certain amount of time (from 1 to 30 minutes), an event occurs.  I then run a very large number of trials, and record how long it takes the event to occur for each trial.  This raw data is then reduced to a set of 30 data points where the x value is the number of minutes it took for the event to occur, and the y value is the percentage of trials which fell into that bucket.  I do not have access to the original data.
How can I use this set of 30 points to identify an appropriate probability distribution which I can then use to generate representative random samples?
I feel like scipy.stats has all the tools I need built in, but for the life of me I can't figure out how to go about it. Any tips?