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Using GPU Simulation to Accurately Fit to the Power-Law Distribution

Efstratios Rappos, Stephan Robert
Institut des technologies de l’information et de la communication, Haute Ecole d’Ingenierie et de Gestion du Canton de Vaud (HEIG-VD), Haute Ecole Specialisee de Suisse occidentale
arXiv:1305.6738 [stat.CO], (29 May 2013)

@article{2013arXiv1305.6738R,

   author={Rappos}, E. and {Robert}, S.},

   title={"{Using GPU Simulation to Accurately Fit to the Power-Law Distribution}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1305.6738},

   primaryClass={"stat.CO"},

   keywords={Statistics – Computation, Computer Science – Distributed, Parallel, and Cluster Computing, Physics – Computational Physics, Physics – Data Analysis, Statistics and Probability, Statistics – Applications, 62F03, 68W10, 62P10, 62P30, 62P35, 62Q05},

   year={2013},

   month={may},

   adsurl={http://adsabs.harvard.edu/abs/2013arXiv1305.6738R},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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This article describes a methodology for fitting experimental data to the discrete power-law distribution and provides the results of a detailed simulation exercise used to calculate accurate cutoff values used to assess the fit to a power-law distribution when using the maximum likelihood estimation for the exponent of the distribution. Using massively parallel programming computing, we were able to accelerate by a factor of 60 the computational time required for these calculations across a range of parameters and construct a series of detailed tables containing the test values to be used in a Kolmogorov-Smirnov goodness-of-fit test, allowing for an accurate assessment of the power-law fit from empirical data.
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