  We study an effect of inhomogeneity of density distribution of the Universe.
We propose a new Lagrangian perturbation theory with a backreaction effect by
inhomogeneity. The inhomogeneity affects the expansion rate in a local domain
and its own growing rate. We numerically analyze a one-dimensional
plane-symmetric model, and calculate the probability distribution functions
(PDFs) of several observed variables to discuss those statistical properties.
We find that the PDF of pairwise peculiar velocity shows an effective
difference from the conventional Lagrangian approach, i.e. even in
one-dimensional plane symmetric case, the PDF approaches an exponential form in
a small relative-velocity region, which agree with the N-body simulation.
