  In the stochastic frontier model, the composed error term consists of the
measurement error and the inefficiency term. A general assumption is that the
inefficiency term follows a truncated normal or exponential distribution. In a
wide variety of models evaluating the cumulative distribution function of the
composed error term is required. This work introduces and proves four
representation theorems for these distributions - two for each distributional
assumptions. These representations can be utilized for a fast and accurate
evaluation.
