  Lensing effects on light rays from point light sources, such like Type Ia
supernovae, are simulated in a clumpy universe model. In our universe model, it
is assumed that all matter in the universe takes the form of randomly
distributed objects each of which has finite size and is transparent for light
rays. Monte-Carlo simulations are performed for several lens models, and we
compute probability distribution functions of magnification. In the case of the
lens models that have a smooth density profile or the same degree of density
concentration as the spherical NFW (Navarro-Frenk-White) lens model at the
center, the so-called gamma distributions fit well the magnification
probability distribution functions if the size of lenses is sufficiently larger
than the Einstein radius. In contrast, the gamma distributions do not fit the
magnification probability distribution functions in the case of the SIS
(Singular Isothermal Sphere) lens model. We find, by using the power law cusp
model, that the magnification probability distribution function is fitted well
using the gamma distribution only when the slope of the central density profile
is not very steep. These results suggest that we may obtain information about
the slope of the central density profiles of dark matter halo from the lensing
effect of Type Ia supernovae.
