Prioritized Experience Replay - why to approximate the Density Function?
That's because the probablity density function might not follow an exponential curve, especially if formula is not $p=1/rank$ but is instead proportional to the amount of error. This will be a byproduct of us not keeping the array sorted, because we want to simplify our life. The curve could then look like this:  

Here, area under the curve is one, but the curve is not exponential or linear or linear-horizontal.

Roll a dice from 0.0 to 1.0, which by the way has the same probability to roll 0.71 as 0.92 etc. Select an element from the array (doesn't have to be sorted!), scanning the array from left to right. 

Consider array with 4 numbers:  {5, 15, 25, 10}. Each represents a portion from  the total sum: 

|0.1|     0.3     |           0.5           |0.2|
you got to be pretty lucky to land on 0.1 (within first 10% segment)


The likelyhood of selecting an element is dependant on its "height under the curve". The taller the element, the more likely for our 0-to-1 counter to land on it.

You can't represent such "landing probability mechanism" by the "exponential dice approach" mentioned in my original question.

However, selecting by the "exponential dice" - albeit not precise might nonetheless work. The only caveat is the array's would have to be kept ordered, which is a pain in the rear. So the benefit isn't really there, just keep the array unsorted and go with the "segmented tree" aka "sum tree" approach O(logn) cost on all operations. This would allow you to avoid scanning the array left-to-right, helping you get from O(N) to O(logn) sampling performance

Now please help me with this question instead :)