Multiplicative processes and power laws in human reaction times derived from hyperbolic functions

In sensory psychophysics reaction time is a measure of the stochastic latency elapsed from stimulus presentation until a sensory response occurs as soon as possible. A random multiplicative model of reaction time variability is investigated for generating the reaction time probability density functions. The model describes a generic class of hyperbolic functions by Piéronʼs law. The results demonstrate that reaction time distributions are the combination of log-normal with power law density functions. A transition from log-normal to power law behavior is found and depends on the transfer of information in neurons. The conditions to obtain Zipfʼs law are analyzed.

► I have examined human reaction time variability by random multiplicative processes.
► A transition from power law to log-normal distributions is described.
► The transition depends on the transfer of information in neurons.
► Zipfʼs law in reaction time distributions depends on the exponent of Piéronʼs law.