The concept of probability distribution plays a centrol role in mathematical statistics and probability theory. The application of this concept to physical problems can be found in equilibrium statistical mechanics or thermodynamics [1–3], the kinetic theory of gas [1,2], the size distributions of colloidal particles and polymers [4,5], polymer configuration [6], etc. However, the extent of using the distribution formalism varies from one application to another Surprisingly, statistical mechanics appears to be the least in adopting such a formalism [7], as reflected in its dealing with the fundamental distributions in an ensemble.