Generating non- normal stable variates using limit theorem properties

Stable distributions share with the normal the property of having a domain of attraction. Here we consider using this property to generate non-normal stable variables in the same way as is commonly done for normal variables. Several types of summands are investigated in a Monte Carlo study and in particular it is shown that one of these provides satisfactory random values for several symmetric stable distributions with finite mean and different characteristic exponents. A comparison with other techniques shows that this method is comparable in speed to the new generator proposed by Chambers et al. (1976) but both methods are slower than the inverse transformation technique. For the special case of the Cauchy distribution a number of easily programmed generators are suggested