I have a question on trying to reverse engineer the probability density function from which a set of numbers were generated. My setup is the following:
1) I have two probability density functions, both of whose domain is bounded in [0,1]: a) Beta (4,2) distribution b) Uniform (0.358060,0.975273) distribution
2) Note that the parameters of the Uniform distribution have been carefully selected so that it has the same mean and variance as the Beta distribution.
3)From each distribution we generate 50 numbers
4)We then sum these random numbers separately (for the beta and uniform) and the value are placed as elements in two vectors (RandBeta and RandUnif).
5)We repeat steps 3-4 until the vectors RandBeta and RandUnif have 20,000 elements each.
In light of the Central Limit Theorem (which would hold for summing variates drawn from the two distributions above) my question is whether it is possible to examine the vectors RandBeta and RandUnif (without knowing which is which) and determine which was generated from the Beta pdf and which form the Uniform pdf?