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Range-Renewal Processes: SLLN, Power Law and Beyonds
Range-renewal SLLN Power Law Small World Regular Varying
2013/6/14
Given $n$ samples of a regular discrete distribution $\pi$, we prove in this article first a serial of SLLNs results (of Dvoretzky and Erd\"{o}s' type) which implies a typical power law when $\pi$ is ...
Using GPU Simulation to Accurately Fit to the Power-Law Distribution
Zipf distribution power law Kolmogorov-Smirnov test parallel computing simulation graph-ics processing unit programming
2013/6/14
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 v...
Power-law of Aggregate-size Spectra in Natural Systems
aggregate-size fractal dimension river basins networks systems allometry
2013/4/28
Patterns of animate and inanimate systems show remarkable similarities in their aggregation. One similarity is the double-Pareto distribution of the aggregate-size of system components. Different mode...
Power-law distributions in binned empirical data
power-law distribution heavy-tailed distributions model selec-tion binned data
2012/9/18
Many man-made and natural phenomena, including the intensity of earthquakes, population of cities, and size of international wars, are believed to follow power-law distributions. The accurate identifi...
Black swans or dragon kings? A simple test for deviations from the power law
Black swans or dragon kings the power law A simple test for deviations
2011/3/25
We develop a simple test for deviations from power law tails, which is based on the asymptotic properties of the empirical distribution function. We use this test to answer the question whether great ...
Power-law distributions in empirical data
Power-law distributions Pareto Zipf maximum likelihood heavy-tailed distributions likelihood ratio test model selection
2010/4/29
Power-law distributions occur in many situations of scientific interest and have
significant consequences for our understanding of natural and man-made phenomena. Unfortunately,the detection and char...