This paper aims at merging five gridded products of monthly aerosol optical depth (AOD), namely, MERRA-2, MISR, MODIS-Terra, MODIS-Aqua, and VIIRS, over a period of eight years, from 2012 March to 2020 February. Since these individual products offer alternative realizations of the same underlying AOD process, it is beneficial to study them collectively. To that effect, several parametric and nonparametric regressions, including ensemble model output statistics, quantile regression, quantile regression neural network, and quantile regression forest, are used to optimally combine these products. These regressions generate predictive distributions or quantiles, and thus can be thought of as probabilistic merging or fusion tools. As compared to traditional merging or fusion techniques, which only issue single-valued predictions of AOD, the present ones allow the final AOD product to carry a notion of probability, which is essential for uncertainty quantification. To assess the quality of the final AOD product with respect to that of the individual products, this study employs the important, yet often overlooked, distribution-oriented verification approach. In addition, the calibration and sharpness of the predictive distributions issued by different merging techniques are compared using two strictly proper scoring rules, as well as appropriate graphical tools. Overall, a significant reduction (13%) in root mean square error is achieved by the best merging method (quantile regression forest) compared to the best original dataset (MERRA-2). A significant reduction in bias is also achieved with respect to the MODIS and VIIRS databases, and even more so, to MISR's.