Adaptive Applications of Maximum Entropy Principle

Abstract

The probability distribution of a system can be adaptively derived using the maximum entropy principle subject to its information set in terms of probabilistic moments. The obtained probability distribution characterizes the wide range of exponential family of distributions when one maximizes Shannon entropy. On maximizing Tsallis entropy with non-extensive parameter q, power law distributions are obtained which portrays the well-known Shannon family of exponential distribution as, \(q \to 1\). The maximization of Shannon entropy subject to the shifted geometric mean constraints leads to a probability distribution in terms of Hurwitz zeta function. This density characterizes the equilibrium state of broadband network traffic. Moreover, maximization of Shannon entropy in Laplace domain subject to specific constraints provides a transient probability distribution which characterizes the behavior of M/M/1/1 queueing system.