In this paper, we propose a method for a quantitative analysis of melanin and hemoglobin pigments from the skin color images. In the previous paper, we proposed a method to extract the values of melanin and hemoglobin components assuming a modified Lambert-Beer law in a linear density space. However, these extracted components are not quantitative values, since the modified Lambert-Beer law is based on the strong approximation of optical scattering process. In the proposed method for the quantitative analysis, the optical scattering process is well approximated in a nonlinear density space. The skin colors are on the two dimensional plane in the nonlinear density space, which is spanned by melanin and hemoglobin vectors. It is found that the components for the melanin and hemoglobin vectors are related to density and root of density, respectively. The proposed method was applied to the skin color image of arm irradiated by UV-B, and the results show the effectiveness of the proposed method.