  We study several anisotropic inflationary models and their implications for
the observed violation of statistical isotropy in the CMBR data. In two of
these models the anisotropy decays very quickly during the inflationary phase
of expansion. We explicitly show that these models lead to violation of
isotropy only for low l CMBR modes. Our primary aim is to fit the observed
alignment of l=2,3 multipoles to the theoretical models. We use two measures,
based on the power tensor, which contains information about the alignment of
each multipole, to quantify the anisotropy in data. One of the measures uses
the dispersion in eigenvalues of the power tensor. We also define another
measure which tests the overall correlation between two different multipoles.
We perturbatively compute these measures of anisotropy and fix the theoretical
parameters by making a best fit to l=2,3 multipoles. We show that some of the
models studied are able to consistently explain the observed violation of
statistical isotropy.
