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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...
Strong Law of Large Numbers Under a General Moment Condition
quasi-stationary sequence strong law of large numbers maximum inequality
2009/4/27
We use our maximum inequality for p-th order random variables (p>1) to prove a strong law of large numbers (SLLN) for sequences of p-th order random variables. In particular, in the case p=2 our resu...