On the generation of random numbers from heavy-tailed distributions

A method is described for the generation of random numbers using a modification of the rejection technique, which is useful when the inverse of the underlying probability distribution function is inexpressable or is expensive to compute. However, the rejection technique can also be expensive if the underlying distribution has heavy tails. The method proposed reduces this expense by computing the random variate from a subinterval of the range space which is chosen randomly. The method is illustrated for a set of parameterized density functions. This technique has proven to be effective for investigating the robust smoothing properties of a class of nonlinear digital filters by Monte Carlo simulation.<>