Revisiting power-law estimation with applications to real-world human typing dynamics

Ubiquitous use of smartphones has significantly shaped interpersonal communications in modern life, in particular interactions via text messaging. To study the underlying dynamics of these smartphone-based human communications, we used a unique smartphone typing dataset that was passively and unobtrusively collected in-the-wild from 296 users via a custom-made iPhone keyboard. To reliably and accurately characterize the underlying distribution of the inter-event time between two consecutive keypresses, we (i) developed a statistical approach that integrates existing methods for estimating power-law distribution, and (ii) showed that power-law is a plausible candidate to represent human typing dynamics. We designed synthetic-data simulations in multiple scenarios where the synthetic data may or may not imitate human typing characteristics. Using numerical simulations, we showed that our approach, in all scenarios, improves the accuracy and stability of power-law estimates upon the common methods. We further demonstrated that when the synthetic data follow human typing characteristics, common methods lead to significant misestimations of power-law exponent as they fail to take into account the key characteristics of the observed data. More broadly, our approach applies beyond the power-law estimation for human typing dynamics data.