Abstract <p>The paper examines the possibility of analytically approximating the neutrino distribution function in a core-collapse supernova. A minimal model of this distribution function, dependent on four parameters, was constructed. Three approximations of the spectral and angular neutrino distributions within the model are considered. The parameters of these approximations were obtained using the results of numerical simulations of Prometheus-Vertex code. Analysis of their accuracy made it possible to construct two neutrino distribution functions with higher accuracy, respectively, inside and outside of the protoneutron star. This model was extended by adding to the main neutrino radiation a contribution from a neutrino halo, which appears in the supernova in the region behind the shock wave. Its minimal model required the introduction of two additional parameters for the overall distribution function in this part of the supernova. Based on the results obtained for a minimal model of the neutrino distribution function in the supernova envelope, radial fits of its parameters, including parameters of neutrino halo, were obtained. An attempt was made to find a correlation of these parameters with the characteristic spatial scales of the supernova. Within this problem, a fairly complete set of these quantities was calculated. Analysis of their correlation with the radial approximation of neutrino parameters was performed. An expression for the distribution of main neutrino emission in the supernova envelope was obtained as a function of luminosity, neutrino average energy, and the radii of the protoneutron star core and the neutrinosphere for electron neutrinos. The contribution of the neutrino halo is presented as a function of the shock wave position and the obtained coefficient of halo amplitude, which depends on the supernova model.</p>