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.
As a specific procedure, first, we roughly search for the starting point of the downtrend using the 13-point moving median to avoid being fooled by local trends
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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.