Velocity fluctuations at 1 m and 5 m below pack-ice drifting at an average speed of 15 cm s-1 are analyzed to describe the conditional statistics of Reynolds stress in the under-ice boundary layer, under melting conditions. The fractional contributions to the Reynolds stress show that ejection and sweep events dominate over interaction events. The sweeps are found to be more intense close to the boundary where the third and higher order moments are most pronounced. Third order cumulant expansions are found to describe the conditional Reynolds stress statistics reasonably well. Existing models for the turbulent kinetic energy transport term using cumulant expansion methods capture the effect of observed increase in the friction velocity with depth.