The statistics of real world images have been extensively investigated, but in virtually all cases using only low dynamic range image databases. The few studies that have considered high dynamic range (HDR) images have performed statistical analyses categorizing images as HDR according to their creation technique, and not to the actual dynamic range of the underlying scene. In this study we demonstrate, using a recent HDR dataset of natural images, that the statistics of the image as received at the camera sensor change dramatically with dynamic range, with particularly strong correlations with dynamic range being observed for the mean, standard deviation, skewness and kurtosis, while the one over frequency relationship for the power spectrum breaks down for images with a very high dynamic range, in practice making HDR images not scale invariant. Effects are also noted in the derivative statistics, the single pixel histograms and the Haar wavelet analysis. However, we also show that after some basic early transforms occurring within the eye (light scatter, non-linear photoreceptor response, center-surround modulation) the statistics of the resulting images become virtually independent from the dynamic range, which would allow them to be processed more efficiently by the human visual system.