MAXIMAL NON-SYMMETRIC ENTROPY LEADS NATURALLY TO ZIPF'S LAW

As the most fundamental empirical law, Zipf's law has been studied from many aspects. However, its meaning is still an open problem. Some models have been constructed to explain Zipf's law. In the letter, a concept of auxiliary information of an event is introduced, and a new entropy named non-symmetric entropy is defined. We prove that maximizing non-symmetric entropy leads naturally to Zipf's law under the special auxiliary information parameters. At the same time, if we take other auxiliary parameters we will get other distribution laws.