I have two variables, x1 and x2, which are sampled from two Gaussian distributions respectively.
I created an iteraction term x3 which is x1 multiply x2. Not surprisingly, x3 has very fat tail, ie., the value stretches far into right end and left end of x-axis.
Although linear regression does not equire x3 to be Gaussian, I still would 'cut' those very large values of x3
Obviously I can simply put a cap. But I am wondering if there is a way to systematically 'concentrate' all the x3 values towards 0
I have tried to take square root of x3 , for those negative x3, I use -1 * sqrt(x3*-1) . However, the result has two bells, one for positive and one for negative. I am wondering if there is a better way to 'contentrate' x3 that produces a distribution similar to Gaussian (I don't need it to be exactly Gaussian) , can someone share some idea?