  We propose a novel method for testing isotropy of a three-dimensional
distribution using Shannon entropy. We test the method on some Monte Carlo
simulations of isotropic and anisotropic distributions and find that the method
can effectively identify and characterize different types of hemispherical
asymmetry inputted in a distribution. We generate anisotropic distributions by
introducing pockets of different densities inside homogeneous and isotropic
distributions and find that the proposed method can effectively quantify the
degree of anisotropy and determine the geometry of the pockets introduced. We
also considered spherically symmetric radially inhomogeneous distributions
which are anisotropic at all points other than the centre and find that such
anisotropy can be easily characterized by our method. We use a semi analytic
galaxy catalogue from the Millennium simulation to study the anisotropies
induced by the redshift space distortions and find that the method can separate
such anisotropies from a general one. The method may be also suitably adapted
for any two dimensional maps on the celestial sphere to study the hemispherical
asymmetry in other cosmological observations.
