Inference of network internal link statistics has become an important condition for operating and evaluating large-scale telecommunication networks. Since it is not realistic to directly monitor each link along some specific path, so end-to-end probes are used to collect the network link statistics at terminal nodes of the network. This paper uses an unicast probing method to infer the link delay statistics. This paper proposes a bias corrected estimator for the internal link delay cumulant generating function (CGF) based on unicast probe end-to-end delay measurements. This paper shows that the proposed estimator obtains the smaller mean square error comparable to link delay CGF estimates obtaines from directly measured link delay statistics.