MATLAB's $\tt dsp.ParametricEQFilter$ bandwidth question
Apparently, after some research, I have found that the bandwidth "bandedges" is a bit of a tricky subject: (see Bandwidth Re-visited).
Some references suggest indeed that the bandwidth is measured at the gain which is equal to half of the peak gain. Some others say that you should measure the bandwidth at $ +3\ \textrm{dB}$ for boost gain, $ -3\ \textrm{dB}$ for cut. (which eventually runs into the issue of where it should be measured if the gain is less than $ 3\ \textrm{dB}$.

Hilmar is right about the geometric mean of the corner frequencies. However, the cutoff points (i.e. the bandedges) do not exist at half the peak gain in MATLAB.   They exist at $G^{2}_B = \frac{1+G^2}{2}$, where $G$ is the parametric equalizer linear gain, and $G_B$ is the linear bandwidth gain as described here.