Augment a sample to improve goodness-of-fit

#1
Hi all,

Lets say I have a sample from a normal (or any other) distribution, and the goodness-of-fit is reasonable. It is possible to improve this goodness-of-fit by sampling one more "good" variate. What about these "good" variates? How can I find one without trial-and-error? Even better, is it possible to construct their (conditional) probability distribution?

Thank you