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

TL;DR

This paper derives analytic expressions for the cumulative distribution function of the composed error term in stochastic frontier models, assuming truncated normal or exponential inefficiencies, enabling faster and more accurate evaluations.

Contribution

It introduces four new representation theorems for the CDF of the composed error term under common inefficiency distributions, improving computational efficiency.

Findings

Provides explicit formulas for the CDF under both distributions.

Enables faster evaluation of stochastic frontier models.

Improves accuracy in efficiency measurement calculations.

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.