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ON THE PERFORMANCE OF KOLMOGOROV‐SMIRNOV TESTS ON STABLE RANDOM VARIABLES 1
Author(s) -
Hua Tsushung A.
Publication year - 1985
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1985.tb00571.x
Subject(s) - kolmogorov–smirnov test , mathematics , statistics , random variable , cumulative distribution function , transformation (genetics) , variable (mathematics) , representation (politics) , sample (material) , statistical physics , statistical hypothesis testing , probability density function , mathematical analysis , physics , law , thermodynamics , biochemistry , chemistry , politics , political science , gene
Summary 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.