  Recent numerical simulations have shown that the distribution of conductance
P(g) in 3D strongly localized regiem differs significally from the expected log
normal distribution. To understand the origin of this difference analytically,
we used a generalized DMPK equation for the joint probablity distribution of
the transmission eigenvalues which includes a phenomenological (disorder and
dimensionality dependent) matrix K containing certain correlations of the
transfer matrices. We first of all examine the assumptions made in the
derivation if the generalized DMPK and find that to a good approximation they
remain valid in 3D. We then evaluate the matrix K numerically for various
strength of the disorder and various system sizes. In the strong disorder limit
we find that K can be described by a simple model which, for a cubic system,
depends on a single parameter. We use this phenomenological model to
analytically evaluate the full distribution P(g) for Anderson insulators in 3D.
The analytic results allow us to develop an intuitive understanding of the
entire distribution, which differs qualitatively from the log-normal
distribution of a Q1D wire. We also show that out method could be applicable in
the critical regime of the Anderson transition.
