In-situ measurements of the rest-frame distribution functions of cometary pick-up water-group ions are used to derive the number and energy density of these ions as a function of distance from the Comet Giacobini-Zinner. The observed density profiles are found to be the same in the inbound and outbound passes and their shape is consistent with predictions of a simple model of pick-up ion production from neutrals of a given type which flow radially outward at ~1 km/s and are lost at a rate &lgr;. Comparing predictions of this model with the measured density profiles we find that &lgr;=2.10-6 sec-1 and that the production rate of water-group cometary molecules is 2.6⋅1028/sec. The measured distribution functions of the pick-up water-group ions may be represented by a two-segment power-law with a break at an energy EB~20 keV, corresponding to a speed, VB=438 (E/M)1/2, of ~500 km/s at distances greater than ~10-5 km. The shapes of the distribution functions indicate that the interaction process of the solar wind with cometary ions is predominantly stochastic.