Has someone an idea how to create a hysteresis plot that models a system with hysteresis?

A simple plot can be created by plotting two arctan functions (g1,g2)

But, I'd rather need a continous function as in the second example (f1..3).

My problem is in statistics. I'm looking for the resulting normalized distribution funtion.

Given a sample has a normal distribution of trait A, and given a subgroup that posseses trait B with a different normal distribution of trait A. Waht would the distribution of trait A be if we eliminate the subgroup that posseses trait B.

The following example that assumes a subgroup of 20% does not yield the proper result.

Very likely there is a very simple solution to this question, but I searched Maple's help pages and this forum and didn't find a solution.  Probably because I don't use the correct English terms.

given two functions

(1) X := x->f1(t);

(2) Y := y->f2((t);

witth t = -infinity...infinity; f1 and f2 arbitrary functions of a parameter t

How I can get the function

Y := x->f3(x);