The statistical model modified to include resonant interaction is discussed. It is shown that arbitrary mass-squared distributions calculated from Lorentz invariant phase space can be expressed as a product of two phase-space factors. Expressions arising in the modified model are reduced to either products of phase-space factors or simple integrals over such products. Application to nucleon-antinucleon annihilation into pions is given. Results are presented for the reaction p+-p→ 2π++2π-+π0 at antiproton momentum 1.61 GeV/c, and the observed three-pion mass distributions are fitted with a half-width for the ω resonance of (10.1±2.9) MeV.