A random variable that depends on the Laudau distribution can be generated by the following method presented by Chambers, Mallows and Stuck.
For the following two independent variables that depend on a uniform distribution without boundary values:
The variables that depend on the stable distribution are obtained as follows:
α ≠ 1:
α = 1:
Since the Landau distribution is a stable distribution with α = 1 and β = 1:
J.M.Chambers, C.L.Mallows; B.W.Stuck, "A Method for Simulating Stable Random Variables" (1976)