Thirty-three fast radio bursts ( FRBs ) had been detected by March 2018 .
Although the sample size is still limited , meaningful statistical studies can already be carried out .
The normalised luminosity function places important constraints on the intrinsic power output , sheds light on the origin ( s ) of FRBs , and can guide future observations .
In this paper , we measure the normalised luminosity function of FRBs .
Using Bayesian statistics , we can naturally account for a variety of factors such as receiver noise temperature , bandwidth , and source selection criteria .
We can also include astronomical systematics , such as host galaxy dispersion measure , FRB local dispersion measure , galaxy evolution , geometric projection effects , and Galactic halo contribution .
Assuming a Schechter luminosity function , we show that the isotropic luminosities of FRBs have a power-law distribution that covers approximately three orders of magnitude , with a power-law index ranging from -1.8 to -1.2 and a cut off \sim 2 \times 10 ^ { 44 } \mathrm { erg } \mathrm { s } ^ { -1 } .
By using different galaxy models and well-established Bayesian marginalisation techniques , we show that our conclusions are robust against unknowns , such as the electron densities in the Milky Way halo and the FRB environment , host galaxy morphology , and telescope beam response .