Various models based on measure-correlate-predict (MCP) methods have been used to estimate the long-term wind turbine power output (WTPO) at target sites for which only short-term meteorological data are available. The MCP models used to date share the postulate that the influence of air density variation is of little importance, assume the standard value of 1.225 kg m(-3) and only consider wind turbines (WTs) with blade pitch control. A performance assessment is undertaken in this paper of the models used to date and of newly proposed models. Our models incorporate air density in the MCP model as an additional covariable in long-term WTPO estimation and consider both WTs with blade pitch control and stall-regulated WTs. The advantages of including this covariable are assessed using different functional forms and different machine learning algorithms for their implementation (Artificial Neural Network, Support Vector Machine for regression and Random Forest). The models and the regression techniques used in them were applied to the mean hourly wind speeds and directions and air densities recorded in 2014 at ten weather stations in the Canary Archipelago (Spain). Several conclusions were drawn from the results, including most notably: (a) to clearly show the notable effect of air density variability when estimating WTPOs, it is important to consider the functional ways in which the features air density and wind speed and direction intervene, (b) of the five MCP models under comparison, the one that separately estimates wind speeds and air densities to later predict the WTPOs always provided the best mean absolute error, mean absolute relative error and coefficient of determination metrics, independently of the target station and type of WT under consideration, (c) the models which used Support Vector Machines (SVMs) for regression or random forests (RFs) always provided better metrics than those that used artificial neural networks, with the differences being statistically significant (5% significance) for most of the cases assessed, (d) no statistically significant differences were found between the SVM- and RF-based models.