The traditional ocean color remote sensing usually focuses on using optical inversion models to estimate the properties of in-water components from the above-surface spectra, so we call it the spectrum-concentration (SC) scheme. Unlike the SC scheme, this study proposed a new research scheme, distribution-distribution (DD) scheme, which uses statistical inference models to estimate the possibility distribution of these in-water components, based on the possibility distribution of the observed spectra. The DD scheme has the advantages that (1) it can rapidly give the key and overview information of the interest water, instead of using the SC scheme to compute each image pixel, (2) it can assist the SC scheme to improve their models and parameters, and (3) it can provide more valuable information for better understanding and indicating the features and dynamics of aquatic environment. In this study, based on Landsat-8 images, we analyzed the spectral possibility distributions (SPD) of 688 global water and found many of them were normal, lognormal, and exponential distributions, but with diverse patterns in distribution parameters such as the mean, standard deviation, skewness and kurtosis. Furthermore, we used Monte-Carlo and Hydrolight simulations to study the theoretical and statistical connections between the possibility distributions of in-water components and SPDs. The simulation results were basically consistent with the observations on the real water. Then by using the simulation and field measured data, we proposed a bootstrap-based DD scheme and developed some simple statistical inference models to estimate the distribution parameters of yellow substance in lakes. Since DD scheme is still on its early stage, we also suggested some potential and useful topics for the future work.