Solar dishes concentrate the quasi-collimated sun light towards a focal point. Typically, the optical characterization consists of experimental flux map measurements and Monte-Carlo ray-tracing (MCRT) simulations, which are fitted based on experimental data and serve for the prediction of the distribution of the irradiation in receivers or reactors. However, the MCRT simulations usually rely on idealized mirror geometries (i.e. parabolic mirrors), neglecting the actual dish geometry resulting from its construction method (such as petals, facets or segments). Thus, the parameter fitting might yield unrealistic parameters and local radiative flux peaks ("hot spots"), which are often experimentally detected behind the focal plane, cannot be predicted. Here, we characterized the 7m diameter solar dish at EPFL comprising 27 petals with a nominal focal length of 3.8 m and a rim angle of 50.3°. The measured peak concentration was 1781 suns and the received integrated solar power was 20.0 kW over an 18 cm diameter spot. We proposed an advanced geometry approach for the MCRT model considering the curvature of the dish, i.e. geometries mathematically described by a parabola with an exponent not equal, but close to 2. The advanced geometry approach was then applied for predicting experimentally measured flux distribution in focal and off-focus planes. The fitted reflectivities were 70% and 86% for the idealized and advanced geometry approach, respectively. The idealized geometry approach found an unrealistically low value whereas the advanced geometry approach's value was within 1% of the manufacturer's specification. The advanced geometry approach predicted a parabola exponent of 1.94, which emphasizes that the best geometry to describe the solar dish deviates from a perfect paraboloid. We conclude that MCRT models should consider non-perfect parabolic geometries for solar dishes in order to obtain more realistic values for the fitted parameters.