A piecewise power-law model with shape parameter alpha, growth rate R, and duration T describes word diffusion, with large-scale blog and search data showing alpha mode near 0.5 and sub-exponential growth in 55% of 2,963 analyzed patterns.
A standard symmetric error measure (like least squares, (𝑦 𝑡 −ˆ𝑦(𝑡))2) would be pulled upward unfairly by these large spikes (outliers)
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Sub-exponential Growth Dynamics in Complex Systems: A Piecewise Power-Law Model for the Diffusion of New Words and Names
A piecewise power-law model with shape parameter alpha, growth rate R, and duration T describes word diffusion, with large-scale blog and search data showing alpha mode near 0.5 and sub-exponential growth in 55% of 2,963 analyzed patterns.