Blazars are known to show periods of quiescence followed by outbursts visible throughout the electromagnetic spectrum. We present a novel maximum likelihood approach to capture this bimodal behaviour by examining blazar radio variability in the flux-density domain. We separate quiescent and flaring components of a source's light curve by modelling its flux-density distribution as a series of 'off'- and 'on'-states. Our modelling allows us to extract information regarding the flaring ratio, duty cycle, and the modulation index in the 'off'state, in the 'on'- state, as well as throughout the monitoring period of each blazar. We apply our method to a flux-density-limited subsample from the Owens Valley Radio Observatory's 15 GHz blazar monitoring programme, and explore differences in the variability characteristics between BL Lacs and FSRQs as well as between gamma-ray detected and non-detected sources. We find that (1) BL Lacs are more variable and have relatively larger outbursts than the FSRQs; (2) unclassified blazar candidates in our sample show similar variability characteristics as the FSRQs and (3) gamma-ray detected differ from the gamma-ray non-detected sources in all their variability properties, suggesting a link between the production of gamma-rays and the mechanism responsible for the radio variability. Finally, we fit distributions for blazar flaring ratios, duty cycles, and on- and off-modulation indices that can be used in population studies of variability-dependent blazar properties.