The following problem came up on the Mathematica forum as "Generating a list of integers that roughly satisfy a distribution": Given $n$, find $n$ integers (possibly with duplicates) whose distribution approximates a given normal distribution.
For example, given a normal with mean 25 and standard deviation 7, the following multiset could be a decent candidate :
I understand that the term "approximates" is not properly defined and there may be several ways of fixing that. For example, one could specify that random samples taken from the discrete distribution should "look like" (again, need to specify what "looks like means") they are drawn from the continuous distribution (conditioning the normal distribution on integrality or after rounding).
Are there references on that problem?