The statistics of clear-sky index can be used to determine solar irradiance when the theoretical clear sky irradiance and the cloud cover are known. In this paper, observations of hourly clear-sky index for the years of 2010-2013 at 63 locations in the UK are analysed for over 1 million data hours. The aggregated distribution of clear-sky index is bimodal, with strong contributions from mostly-cloudy and mostly clear hours, as well as a lower number of intermediate hours. The clear-sky index exhibits a distribution of values for each cloud cover bin, measured in eighths of the sky covered (oktas), and also depends on solar elevation angle. Cloud cover is measured either by a human observer or automatically with a cloud ceilometer. Irradiation (time-integrated irradiance) values corresponding to human observations of "cloudless" skies (0 oktas) tend to agree better with theoretical clear-sky values, which are calculated with a radiative transfer model, than irradiation values corresponding to automated observations of 0 oktas. It is apparent that the cloud ceilometers incorrectly categorise more non-cloudless hours as cloudless than human observers do. This leads to notable differences in the distributions of clear-sky index for each okta class, and between human and automated observations. Two probability density functions the Burr (type III) for mostly-clear situations, and generalised gamma for mostly-cloudy situations are suggested as analytical fits for each cloud coverage, observation type, and solar elevation angle bin. For human observations of overcast skies (8 oktas) where solar elevation angle exceeds 10, there is no significant difference between the observed clear-sky indices and the generalised gamma distribution fits. (C) 2017 Elsevier Ltd. All rights reserved.