The plug-in principle is a technique used in probability theory and statistics to approximately compute or to estimate a feature of a probability distribution (e.g., the expected value, the variance, a quantile) that cannot be computed exactly. It is widely used in the theories of Monte Carlo simulation and bootstrapping.
Roughly speaking, the plug-in principle says that a feature of a given distribution can be approximated by the same feature of the empirical distribution of a sample of observations drawn from the given distribution. The feature of the empirical distribution is called a plug-in estimate of the feature of the given distribution. For example, a quantile of a given distribution can be approximated by the analogous quantile of the empirical distribution of a sample of draws from the given distribution.
https://www.statlect.com/asymptotic-theory/plug-in-principle
