ON THE PERFORMANCE OF KOLMOGOROV-SMIRNOV TESTS ON STABLE RANDOM VARIABLES1

This paper provides two procedures to perform the Kolmogorov–Smirnov (K-S) tests on stable random variables. One utilizes the integral representation of the cumulative distribution function of this random variable to perform the K-S test; the other utilizes the Gil-Pelaez-Roseń transformation of data (Csörg(1983)) to test uniformity on (0,1) for the transformed sample. Both procedures are examined and evaluated by a simulation study.