Analytic expressions for the Cumulative Distribution Function of the Composed Error Term in Stochastic Frontier Analysis with Truncated Normal and Exponential Inefficiencies

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.