1 (Couplings and monotonicity). A coupling of two or more random variables is nothing but a simultaneous reconstruction of (copies of) the variables in the same probability model. For example, let X and Y are Bernoulli random variables each taking values 0 and 1 with probability 1/2. We can construct a coupling (X̃, Ỹ ) of X and Y by generating a uniform random variable Z over the set {00, 01, 1...

We propose an exact method for generating random deviates from continuous order statistics. This versatile method that generates Beta deviates as a middle step can be applied to any density function without resorting to numerical inversion. We also conduct an exhaustive investigation to document the merits of our method in generating deviates from any Beta distribution.