(1) You are given a distribution of past outcomes that describe a process. (pic: red dist.)

(2) You collect new data on the same process and get a new distribution of outcomes. (pic: black dist.)

These two distributions turns out to be somewhat different. Is it possible to calculate a distribution of the expected future outcomes needed for the new data (black dist.) to converge and become identical to the old one (red dist.)? If so, how?