  The statistical problem for network tomography is to infer the distribution
of $\mathbf{X}$, with mutually independent components, from a measurement model
$\mathbf{Y}=A\mathbf{X}$, where $A$ is a given binary matrix representing the
routing topology of a network under consideration. The challenge is that the
dimension of $\mathbf{X}$ is much larger than that of $\mathbf{Y}$ and thus the
problem is often called ill-posed. This paper studies some statistical aspects
of network tomography. We first address the identifiability issue and prove
that the $\mathbf{X}$ distribution is identifiable up to a shift parameter
under mild conditions. We then use a mixture model of characteristic functions
to derive a fast algorithm for estimating the distribution of $\mathbf{X}$
based on the General method of Moments. Through extensive model simulation and
real Internet trace driven simulation, the proposed approach is shown to be
favorable comparing to previous methods using simple discretization for
inferring link delays in a heterogeneous network.
