  The most fundamental notion for Hilbert space frames is the sequence of frame
coefficients for a vector x in the space. Yet, we know little about the
distribution of these coefficient sequences. In this paper, we make the first
detailed study of the distribution of the frame coefficients for vectors in a
Hilbert space, as well as the related notion of the square sums of the
distances of vectors in the space from the frame vectors. We will give some
surprisingly exact calculations for special frames such as unit norm tight
frames and equiangular frames. This is a study which should have been done 20
years ago.
