The complete part of the earthquake frequency–magnitude distribution, above the completeness magnitude mc, is well described by the Gutenberg–Richter law. On the other hand, incomplete data does not follow any specific law, since the shape of the frequency–magnitude distribution below max(mc) is function of mc heterogeneities that depend on the seismic network spatiotemporal configuration. This paper attempts to solve this problem by presenting an asymmetric Laplace mixture model, defined as the weighted sum of Laplace (or double exponential) distribution components of constant mc, where the inverse scale parameter of the exponential function is the detection parameter κ below mc, and the Gutenberg–Richter β-value above mc. Using a variant of the Expectation-Maximization algorithm, the mixture model confirms the ontology proposed by Mignan [2012, https://doi.org/10.1029/2012JB009347], The performance of the proposed mixture model is analysed, with encouraging results obtained in simulations and in eight real earthquake catalogues that represent different seismic network spatial configurations.