The current from an array of field emitters is often dominated by a subset of tips. The impact of processes such as, sputtering damage on the evolution of array current can be estimated based on a hyperbolic tip model if the distribution of the emitters in both work function and apex radius can be approximated. In this work, we describe the characterization of emission under the assumptions that (i) the emission site radii are log-normal distributed and (ii) that the degree to which work-function-increasing adsorbates are present is related. to background pressure. These,assumptions generate statistical factors that may be used to generalize a single tip theory to array current estimates via the statistical hyperbolic model. A derivation of the statistical factors are given and the methodology of the hyperbolic model's application explained. The methodology is then applied to analyze experimental data for molybdenum field emitters coated, with ZrC under development for spacecraft electric propulsion and electrodynamics tethers devices.