  Statistical mechanics is generalized on the basis of an additive information
theory for incomplete probability distributions. The incomplete normalization
$\sum_{i=1}^wp_i^q=1$ is used to obtain generalized entropy
$S=-k\sum_{i=1}^wp_i^q\ln p_i$. The concomitant incomplete statistical
mechanics is applied to some physical systems in order to show the effect of
the incompleteness of information. It is shown that this extensive generalized
statistics can be useful for the correlated electron systems in weak coupling
regime.
