where p i (ω) is the dipole moment of particle i. The ensemble extinction spectrum (red curve in Figure ), which is generally smooth and always positive, can be contrasted to a subset of the individual particle spectra (black), which have large variations and can even take on negative values. Just as we define a resonant frequency ω res and spectral linewidth W for the ensemble extinction cross-section, we can define a resonant frequency ω res,i and linewidth W i for each particle's extinction spectrum. The set of ω res,i in the ensemble forms a resonant frequency distribution P (ω res,i ), which we can quantify more reliably in simulations in terms of the cumulative distribution function,