  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
