  We analyze the lineshape of x-ray diffraction profiles of GaN epitaxial
layers with large densities of randomly distributed threading dislocations. The
peaks are Gaussian only in the central, most intense part of the peak, while
the tails obey a power law. The $q^{-3}$ decay typical for random dislocations
is observed in double-crystal rocking curves. The entire profile is well fitted
by a restricted random dislocation distribution. The densities of both edge and
screw threading dislocations and the ranges of dislocation correlations are
obtained.
