Diffusion magnetic resonance imaging (dMRI) is the reference \emph{in vivo} modality to study the connectivity of the brain white matter. Images obtained through dMRI are indeed related to the probability density function (pdf) of displacement of water molecules subject to restricted diffusion in the brain white matter. The knowledge of this diffusion pdf is therefore of primary importance. Several methods have been devised to provide an estimate of it from noisy dMRI signal intensities. They include popular diffusion tensor imaging (DTI) as well as higher-order methods. These approaches suffer from important drawbacks. Standard DTI cannot directly cope with multiple fiber orientations. Higher-order approaches can alleviate these limitations but at the cost of increased acquisition time. In this research report, we propose, in the same vein as DTI, a new parametric model of the diffusion pdf with a reasonably low number of parameters, the estimation of which does not require acquisitions longer than those used in clinics for DTI. This model also accounts for multiple fiber orientations. It is based on the assumption that, in a voxel, diffusing water molecules are divided into compartments. Each compartment is representative of a specific fiber orientation (which defines two opposite directions). In a given compartment, we further assume that water molecules that diffuse along each direction are in equal proportions. We then focus on modeling the pdf of the displacements of water molecules that diffuse only along one of the two directions. Under this model, we derive an analytical relation between the dMRI signal intensities and the parameters of the diffusion pdf. We exploit it to estimate these parameters from noisy signal intensities. We carry out a cone-of-uncertainty analysis to evaluate the accuracy of the estimation of the fiber orientations and we evaluate the angular resolution of our method. Finally, we show promising results on real data and propose a visualization of the diffusion parameters which is very informative to the neurologist.