We present a new, single-parameter distributional specification for the one-sided error components in single-tier and two-tier stochastic frontier models. The distribution has its mode away from zero, and can represent cases where the most likely outcome is non-zero inefficiency. We present the necessary formulas for estimating production, cost and two-tier stochastic frontier models in logarithmic form. We pay particular attention to the use of the conditional mode as a predictor of individual inefficiency. We use simulations to assess the performance of existing models when the data include an inefficiency term with non-zero mode, and we also contrast the conditional mode to the conditional expectation as measures of individual (in)efficiency.

我们为单层和两层随机边界模型中的单侧误差分量提供了一种新的单参数分布规范。分布的模式远离零，可以表示最有可能的结果是非零效率的情况。我们以对数形式提供估计生产量，成本和两层随机边界模型的必要公式。我们特别注意使用条件模式作为个体效率低下的预测指标。当数据包括具有非零模式的无效项时，我们将使用仿真来评估现有模型的性能，并且还将条件模式与条件期望进行对比，以作为对单个（无效）效率的度量。