  It has been suggested that the density of states approach to performing
lattice simulations in QCD with nonzero chemical potential can be modified to
improve the signal to noise ratio by performing a cumulant expansion of the
complex phase of the fermion determinant, and then simplified by truncating the
expansion after the first non-zero cumulant. This truncation corresponds to
approximating the distribution of the complex phase of the fermion determinant
by a Gaussian form. The crucial question is: how large are the other cumulants?
We calculate the distribution of the complex phase from the hadron resonance
gas model and from a combined lattice strong coupling and hopping expansion. In
the case of the hadron resonance gas model the distribution takes a Gaussian
form, but from the strong coupling and hopping expansion there are corrections.
We discuss the implications to lattice simulations.
