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Table 2 Probability functions for different distributions

From: The mobility laws of location-based games

Distribution Probability function P(x)
Power law \(x^{-\alpha }\)
Truncated power law \(x^{-\alpha }e^{-\lambda x}\)
Exponential \(e^{-\lambda x}\)
Stretched exponential \(x^{\beta -1}e^{-\lambda x^{\beta }}\)
Log-normal \(\frac{1}{x}\exp [-\frac{(\ln x-\mu )^{2}}{2\sigma ^{2}}]\)