Despite it is essential to distribution network economics, computing energy loss for most major networks is still a tough task due to the absence of full monitoring. Assume the line current follows a normal distribution, the sum of its square is a linear combination of independent chi-square variables, which follows a generalized noncentral chi-square distribution. Based on this finding, we develop a new probability-based analytical method to estimate distribution network energy losses efficiently. The proposed analytical method requires merely the knowledge of mean and variance of line current as well as the line resistance while provides a closed-form formula of the probability characteristics of energy loss. The method is demonstrated on a three-feeder radial network.