Starting from the master equation for the hierarchical structure of avalanches of a different kind within the frame of the Bak-Sneppen evolution model, we derive the exact formula of the scaling function describing the probability distribution of avalanches. The scaling function displays features required by the scaling ansatz and verified by simulations. Using the scaling function we investigate the avalanche moment, denoted by 〈Sk〉Δf¯. It is found that for any non-negative integer k, 〈Sk〉Δf¯ diverges as Δf−k, which gives an infinite...
