The complexity of the problem of simulating sequences of
-stable random variables results from the fact that there
are no analytic expressions for the inverse
of the
cumulative distribution function. The first breakthrough was made
by Kanter (1975), who gave a direct method for simulating
random variables, for
. It turned out
that this method could be easily adapted to the general case.
Chambers, Mallows, and Stuck (1976) were the first to give the formulas.
The algorithm for constructing a standard stable random variable
, in representation (1.2), is the
following (Weron; 1996):
where
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Given the formulas for simulation of a standard -stable
random variable, we can easily simulate a stable random variable
for all admissible values of the parameters
,
,
and
using the following property: if
then