The physical basis of estimating the raindrop size distribution (dsd) parameters and rain rate using radar polarimetry depends on the models assumed for the dsd, drop axis ratio and drop canting. We use a gamma model for the dsd with 3 parameters (number density mass-weighted mean diameter, and shape parameter), linear model for the drop axis ratio versus D (beta or slope parameter) and Gaussian canting angle distribution (zero mean, variance of canting angle as the parameter). The inclusion of the beta parameter is to account for small deviations in mean axis ratio from equilibrium due to drop oscillations, while the variance of canting angle is to account for canting due to turbulence. We show that under Rayleigh-Gans scattering, the dual-polarized radar variables such as Z_h, Z_dr, K_dp, L_dr and r_co can be approximated by a more natural polynomial form involving the model parameters (as opposed to power law forms). A retrieval method is proposed for estimating the various model parameters, in particular for the dsd and the rain rate. Simulations (with random errors) are conducted to validate the methodology and are compared with other empirical methods.