A new expression of the probability distribution in incomplete statistics and fundamental thermodynamic relations

In order to overcome the limitations of the original expression of the probability distribution appearing in literature of Incomplete Statistics, a new expression of the probability distribution is derived, where the Lagrange multiplier %B% introduced here is proved to be identical with that introduced in the second and third choices for the internal energy constraint in Tsallis' statistics and to be just equal to the physical inverse temperature. It is expounded that the probability distribution described by the new expression is invariant through uniform translation of the energy spectrum. Moreover, several fundamental thermodynamic relations are given and the relationship between the new and the original expressions of the probability distribution is discussed.