An intuitive meaning of Bose-Einstein and Fermi-Dirac statistics is obtained by maximizing gamma (uncertainty or randomness) as applied to the number of particles per cell probabilities in the mu phase space. (auth)
We derive Bose-Einstein statistics and Fermi-Dirac statistics by Principle of Maximum Entropy applied to two families of entropy functions different from the Boltzmann-Gibbs-Shannon entropy. These entropy functions are identified with special cases of modified Naudts' ϕ-entropy.