Recent released Planck data and other astronomical observations show that the universe may be anisotropic on large scales. This hints a cosmological privileged axis in our anisotropic expanding universe. This paper proceeds a modified redshift in anisotropic cosmological model as 1 + ˜z(t, ˆp) = a(t0) a(t) (1 − A( ˆn. ˆp)) (where A is the magnitude of anisotropy, ˆn is the direction of privileged axis, and ˆp is the direction of each SNe Ia sample to galactic coordinates) along with anisotropic parameter δ = A( ˆn. ˆp) 1+A( ˆn. ˆp) . The luminosity distance is expanded with model-independent cosmographic parameters as a function of modified redshift ˜z. As the transformation matrix M(n×n) is obtained to convert the Taylor series coefficients of isotropic luminosity distance to corresponding anisotropic parameters. These results culminate the magnitude of anisotropy about | A | 10−3 and the direction of preferred axis as (l, b) , which are consistent with other studies in 1−σ confidence level.
