Image fusion is growing interest in recent years, thanks to the huge amount of data acquired everyday by sensors on board of satellite platforms. The enhancement of the spatial resolution of a multispectral (MS) image through the use of a panchromatic (PAN) image, usually called pansharpening, is getting more and more relevant. In this work, we focus on the problem of the estimation of the injection coefficients that rule the enhancement of the spatial resolution of the MS image by properly adding the PAN details. In particular, a statistical analysis of the residuals coming from the linear multivariate regression between details extracted from the PAN image and the MS image is performed. A novel hybrid model is introduced for accurately describing the statistical distribution of these residuals, together with a procedure for efficiently estimating both the parameters of the residual distribution and the injection coefficients. The improvements achieved by the proposed approach are assessed using two very high resolution datasets acquired by the WorldView-3 and Worldview-4 satellites. The benefits of the proposed approach are particularly clear when vegetated areas are involved in the fusion process.