  Recently we introduced mixed-state localization operators associated to a
density operator and a (compact) domain in phase space. We continue the
investigations of their eigenvalues and eigenvectors. Our main focus is the
definition of a time-frequency distribution which is based on the Cohen class
distribution associated to the density operator and the eigenvectors of the
mixed-state localization operator. This time-frequency distribution is called
the accumulated Cohen class distribution. If the trace class operator is a
rank-one operator, then the mixed-state localization operators and the
accumulated Cohen class distribution reduce to Daubechies' localization
operators and the accumulated spectrogram. We extend all the results about the
accumulated spectrogram to the accumulated Cohen class distribution. The
techniques used in the case of spectrograms cannot be adapted to other
distributions in Cohen's class since they rely on the reproducing kernel
property of the short-time Fourier transform. Our approach is based on quantum
harmonic analysis on phase space which also provides the tools and notions to
introduce the analogues of the accumulated spectrogram for mixed-state
localization operators; the accumulated Cohen's class distributions.
