We use 20 years of Wind solar wind observations to investigate the solar cycle variation of the solar wind driving of the magnetosphere. For the first time, we use generalized quantile-quantile plots to compare the statistical distribution of four commonly used solar wind coupling parameters, Poynting flux, B 2, the ε parameter, and vB ,between the maxima and minima of solar cycles 23 and 24. We find the distribution is multicomponent and has the same functional form at all solar cycle phases; the change in distribution is captured by a simple transformation of variables for each component. The ε parameter is less sensitive than its constituent variables to changes in the distribution of extreme values between successive solar maxima. The quiet minimum of cycle 23 manifests only in lower extreme values, while cycle 24 was less active across the full distribution range
