Entropy of a Zipfian Distributed Lexicon

Abstract: This article presents the calculation of the entropy of a system with Zipfian distribution and shows that a communication system tends to present an exponent value close to one, but still greater than one, so that it might maximize entropy and hold a feasible lexicon with an increasing size. This result is in agreement with what is observed in natural languages and with the balance between the speaker and listener communication efforts. On the other hand, the entropy of the communicating source is very sensitive to the exponent value as well as the length of the observable data, making it a poor parameter to characterize the communication process.