Extended Stevens' power law

An extension of the Stevens' power law, widely used in psychophysics to relate a physical magnitude of a stimulus (e.g. taste, luminance, weight, sound pressure) with the corresponding experienced magnitude (saltiness, brightness, heaviness, loudness etc.) has been proposed. It takes into account the fact that psychophysical functions are basically of a sigmoid and not power-like type. To model the stimulus-response relationship the S-shaped Gompertz function converted to the power form by the mapping procedure is employed. It provides the extended Stevens' power law y(C) = k(C)Cn(C) with the scaling factor k(C) and exponent n(C) as function of the stimulus magnitude C. The model will be used in determination of the saltiness and brightness stimulus-response power function correctly reproducing the experimental psychophysical data in a wide range of the stimuli applied. It will be proven that the extended Stevens' power law belongs to the class of self-similar and allometric processes of the fractal nature.

► An extension of the Stevens' power law is presented. ► The scaling factor and exponent depend on stimulus magnitude. ► The formula reproduces the psychophysical functions of a sigmoid type. ► It describes the class of self-similar and allometric processes of the fractal nature. ► The saltiness and brightness stimulus-response functions are reproduced.