  Four types of explicit estimators are proposed here to estimate the loss
rates of the links in a network with the tree topology and all of them are
derived by the maximum likelihood principle. One of the four is developed from
an estimator that was used but neglected because it was suspected to have a
higher variance. All of the estimators are proved to be either unbiased or
asymptotic unbiased. In addition, a set of formulae are derived to compute the
efficiencies and variances of the estimates obtained by the estimators. One of
the formulae shows that if a path is divided into two segments, the variance of
the estimates obtained for the pass rate of a segment is equal to the variance
of the pass rate of the path divided by the square of the pass rate of the
other segment. A number of theorems and corollaries are derived from the
formulae that can be used to evaluate the performance of an estimator. Using
the theorems and corollaries, we find the estimators from the neglected one are
the best estimator for the networks with the tree topology in terms of
efficiency and computation complexity.
