Depending on the time period and geographical location, the collection of seismic data has been more or less exhaustive and systematic. Thus, seismic catalogues contain some isolated seismic events. This information is usually excluded from the inference process of the recurrence model. In this paper, we assume that earthquakes are modelled by a stationary Poisson point process, under the Gutenberg-Richter assumption. We propose a way to take that information into account by adapting the expression of the likelihood of the Poisson point process. In addition, we consider that the completeness magnitude varies in time.