  Distributed calibration based on consensus optimization is a computationally
efficient method to calibrate large radio interferometers such as LOFAR and
SKA. Calibrating along multiple directions in the sky and removing the bright
foreground signal is a crucial step in many science cases in radio
interferometry. The residual data contain weak signals of huge scientific
interest and of particular concern is the effect of incomplete sky models used
in calibration on the residual. In order to study this, we consider the mapping
between the input uncalibrated data and the output residual data. We derive an
analytical relationship between the input and output probability density
functions which can be used to study the performance of calibration.
