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

Abstract: 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.