  As a technique to investigate link-level loss rates of a computer network
with low operational cost, loss tomography has received considerable attentions
in recent years. A number of parameter estimation methods have been proposed
for loss tomography of networks with a tree structure as well as a general
topological structure. However, these methods suffer from either high
computational cost or insufficient use of information in the data. In this
paper, we provide both theoretical results and practical algorithms for
parameter estimation in loss tomography. By introducing a group of novel
statistics and alternative parameter systems, we find that the likelihood
function of the observed data from loss tomography keeps exactly the same
mathematical formulation for tree and general topologies, revealing that
networks with different topologies share the same mathematical nature for loss
tomography. More importantly, we discover that a re-parametrization of the
likelihood function belongs to the standard exponential family, which is convex
and has a unique mode under regularity conditions. Based on these theoretical
results, novel algorithms to find the MLE are developed. Compared to existing
methods in the literature, the proposed methods enjoy great computational
advantages.
