Blazars are known to show variability on time scales from minutes to years covering a wide range of flux states. Studying the flux distribution of a source allows for various insights. The shape of the flux distribution can provide information on the nature of the underlying variability processes. The level of a possible quiescent state can be derived from the main part of the distribution that can be described by a Gaussian distribution. Dividing the flux states into quiescent and active, the duty cycle of a source can be calculated. Finally, this allows alerting the multi-wavelength and multi-messenger community in case a source is in an active state. To get consistent and conclusive results from flux distributions, unbiased long-term observations are crucial. Only like this is a complete picture of the variability and flux states, e.g., an all-time quiescent state, possible. In seven years of monitoring of bright TeV blazars, the first G-APD Cherenkov telescope (FACT) has collected a total of more than 11,700 hours of physics data with 1500 hours to 3000 hours per source for Mrk 421, Mrk 501, 1ES 1959+650, and 1ES 2344+51.