The use of frequencies well into the EHF band (30-300 GHz) is a key element in 5G and beyond technologies. Rain attenuation is the major impairment affecting terrestrial radio links in this band. In the absence of enough experimental measurements, rain attenuation can be estimated by using physical models of radiowave scattering in rain drops combined with information about the rain Drop Size Distributions (DSD). In this work, the characterization of rain attenuation in the 80-200 GHz frequency range is carried out from a large database of twelve years of experimental DSD gathered in Madrid, Spain. Rain attenuation is estimated for each collected minute of rain using two approaches: a first one based on the assumption of raindrops as spherical and the application of the Mie theory, and a second one that uses a non-spherical raindrop model and electromagnetic simulations and is consequently more realistic. The main results show that the currently used ITU-R model generally underestimates rain specific attenuation; the influence of polarization becomes smaller and negligible as frequency approaches 200 GHz; and rain specific attenuation significantly varies due to the spread of the DSD. Moreover, a model for this variability of rain attenuation is also proposed.