Statistical Simulation

Generate random Numbers from a given distribution $F$ by applying its Quantile Function on a Random Variable $X$ that has Uniform Distribution on $(0,1)$

$$Y:=Q_F^{-}(X):=Q_F^{-}\circ X.$$

$Y$ now has CDF $F$.

This also works the other way around.

How do we get good random numbers from a Uniform Distribution on $(0,1)$?

• random physical process
• deterministic pseudo random numbers
• coin tossing for digits in binary
• erasing leading digits of random numbers with a density