  We theoretically investigate the coefficient of performance (COP) of a
mesoscopic thermoelectric refrigerator realized by using a tunnel junction. We
analyze the influence of particle and heat current fluctuations on the COP out
of the equilibrium regime. We calculate the average COP by using full counting
statistics and find that it depends on the measurement time $\tau$. The
deviation from the macroscopic COP value can be expressed with the Skellam
distribution at all times. This result enables us to improve the Gaussian
approximation valid within the linear response regime, which cannot predict the
average COP in the limit of $\tau \to 0$. We illustrate the time dependence of
the average COP and find that in the short-time regime, the average COP
possesses a minimum. In order to confirm the physical consistency far from
equilibrium, we propose checking the correlation coefficient between the
particle and the heat currents in addition to the positivity of the entropy
production rate.
