M\"ossbauer quadrupole splitting (QS) measurements are reported for ${\mathrm{Fe}}^{57}$ in vitreous YIG (${\mathrm{Y}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$). Electric-field-gradient (EFG) calculations from a computer model of amorphous YIG suggest a distribution $p(|V|)$ of principal EFG components $V$ which peaks at a nonzero value, is asymmetric, and falls off exponentially in the wings. A nonlinear least-squares fit to the QS data using a distribution $p(|V|)$ of Lorentzian lines establishes not only the asymmetry but also the detailed non-Gaussian form of the EFG distribution.