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

Magnification Probability Distribution Functions of Standard Candles in a Clumpy Universe