Possible Size Dependence of Distribution Functions of Classic, Boson, and Fermion Assemblies

I derived the size dependence of distribution function for classic, boson, and fermion assemblies. I did not use the Stirling approximation so that deviation contributed by this approximation at small number of particles can be avoided. I identified that the size dependence of the distribution function is contained in the fermi energy or chemical potential. My results seem to match few reports on the dependence of fermi energy or chemical potential on particle size of several nanometer sized materials