Change distribution of a vector I have the following vector 
my_vector=[0.059; 0.223;0.197;0.176; 0.173; 0.171; 0.0421; 0.209; 0.556;0.252;0.198; 0.255; 0.130; 0.176; 0.110; 0.0845; 0.270; 0.192; 0.199; 0.348]

I want to change the vector in such a way that the output derived vector will have the highest possible distribution change. This means the distribution of the two vectors should be highly different (say have large KLD values) but their distribution should be still from the same family (say the F-test or two-sample K–S test will not reject the hypothesis that they are from the same distribution). 

How could I generate the new vector from the base vector while I meet the constraint (having "highest" "possible" change in distribution)? I need a machine learning (data-driven) method to achieve such a goal.

Thanks in advance for any help and recommendation.
I think the answer(comment) of TwinPenguins provides you a good start. You could improve this by using a Metropolis Monte Carlo approach instead of just trying again and again generating new vectors.
What you could do is:


create a new vector with length similar to yours randomly sampled from the distribution of your interest and compute KLD$_{old}$ (cf. TwinPenguins)
modify this vector and compute KLD$_{new}$.
if (KLD$_{new}$ is better than KLD$_{old}$), the new vector becomes your old vector 
else discard the changes
go back to 2, unless you reach a given target value of KLD


(Note that there may be issues with getting trapped in local minima, but search the Monte-Carlo literature and  you'll find a solution...you can always run multiple times, and then take the best result.)