Abstract: Based on fully relativistic HFS self-consistent field AA model, the emerging probabilities of ionic types are determined in analytic formula using the principle of the maximum entropy, and the ionic structures are obtained in peturbation way. All the contributions from over millions of ionic types are taken into account in statistical method according to convolution principle. Finally the formula of extinction coefficient for bound free transition in hot matter with the statistical effects is given, and some results for iron are discussed.