We briefly review the concept of Renyi information, and discuss the relations to probability distribution function and multi-fractal measures as descriptions of large-scale spatial distribution of galaxies. These measurements can provide complete statistical description by probing the higher moments of the galaxy distribution. A multiplicative cascade simulation can reproduce galaxy distribution with the same statistical high-moment properties. We discuss the potential of the technique. We then present the results of these high-moment measurements for mid-infrared galaxies detected by Infrared Array Camera onboard the Spitzer Space Telescope.