Distribution of the fitted parameters in 1000 realisations of the Cepheid data. The upper three panels show the distributions of a, b (in the P − L relation) and c (the parallax zero-point) for the model in Eq. (7) when extinction is perfectly known (left), and when it has an uncertainty of 0.05 mag (right). The bottom panels show the distribution of c for the model in Eq. (8) when R_V − I is perfectly known (left) and when it has an error of 5% (right). The vertical lines indicate the true values.