Single-molecule spectroscopy of isolated chromophores in solids yields detailed information about the matrix on a microscopic level. In most studies so far, single-molecule (SM) spectra have been characterized by their linewidths. We demonstrate that in a doped amorphous polymer, in which SM excitation spectra generally have a complicated shape, the shapes of SM lines are more fully characterized by their moments than by the usually used linewidth. We present the measured and simulated distributions of the first four moments and of the linewidth for low-temperature spectra of single tetra-tert-butylterrylene molecules embedded in an amorphous poly(isobutylene) matrix. The simulations are based on the standard tunneling model of glasses with appropriate modifications and on a theory of SM line shapes in a disordered host, which was recently derived by Geva and Skinner [J. Phys. Chem. B 101, 8920 (1997)]. The comparative analysis of the measured and simulated distributions allowed us to evaluate the minimal distance of two-level-system-chromphore interactions and the main parameters of the distribution of coupling constants.