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[Bug-gsl] Levý random number generator

From: rafael
Subject: [Bug-gsl] Levý random number generator
Date: Mon, 26 Mar 2007 19:48:01 -0300
User-agent: Internet Messaging Program (IMP) H3 (4.2-cvs)

The Levý skew random number generator (gsl_ran_levy_skew) does not procuce a Levý random number when beta=0 (symmetric case), and the gsl_ran_levy function does not work as stated in the docs. I made some histograms from 10^6 samples to check the accuracy of the algorithms, by comparison agaisnt the numerical integration of the equation of Levý's PDF. For the gsl_ran_levy function there is a good precison for alpha [1,2], for alpha (0.3,1) you must sum a series of random numbers to get the same precision (tipicaly 100 or more gsl_ran_levy numbers). For alpha<=0.3 the algorithm does not work properly, even worse, the error increases as you add more random numbers. This contradicts the manual that says "the algoritm only works for alpha (0,2]". The function gsl_ran_levy_skew does not produce levy random numbers when beta=0, instead the pdf of the random numbers is a linear (?!?!) one.

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