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This paper analyses four statistical distributions used to describe city size distributions: lognormal, double Pareto lognormal, q-exponential, and log-logistic. We use un-truncated city size data for the US, Spain and Italy from 1900 until 2010, and, in addition, the last available year for the remaining countries of the OECD. We estimate the four functions by maximum likelihood. To check the goodness of the fit we use the Kolmogorov- Smirnov and Cramér-von Mises tests, and compute the Akaike information criterion and Bayesian information criterion. The results show that the distribution which best fits data in most of the cases (86.76%) is the double Pareto lognormal. [ABSTRACT FROM AUTHOR]