The maximum likelihood estimation of earthquake hazard parameters (maximum regional magnitude mmax, activity rate λ, and the Gutenberg - Richter parameter b) from incomplete data files is extended to the case of uncertain magnitude values. Two models of uncertainty are considered. In the first one, earthquake magnitude is specified by two values, the lower and the upper magnitude limit. It is assumed that such an interval contains the real, unknown magnitude. In the second model, uncertainty of earthquake magnitude is defined in the same way as it was proposed by Tinti and Mulargia (1985): the departure of the observed (apparent) magnitude from the true, unknown value is distributed normally. The proposed approach allows the combination of catalog parts of different quality, e.g., those where the assessment of magnitude is questionable and those with magnitudes determined very precisely.
As an illustration, the proposed procedures are applied for the estimation of seismicity parameters in western Norway with adjacent sea areas.