随机DEA期望值模型的一些性质

为判别决策单元在随机DEA期望值模型下的随机有效性，首次提出了随机期望无效、随机期望弱有效、随机期望有效以及随机期望超有效的概念．并给出了三个命题用于判别不同显著性水平下随机期望效率与期望效率的关系．在此基础上，得到了两个重要的性质：（1）当期望效率保持不变时，随机期望效率为显著性水平的增函数；（2）当显著性水平保持不变时，随机期望效率为期望效率的增函数．最后，利用随机模拟和一个算例对上述结论进行了验证．

Some properties of the expected value model in stochastic data envelopment analysis

The expected value model in stochastic data envelopment analysis （SDEA） is especially useful for evaluating the efficiency of the decision making units （DMUs） with fixed inputs and stochastic outputs. In this paper, we reinvestigate some properties of this model to extend its potential usage. In order to identify the type of the DMUs＇ efficiency of the expected value model in SDEA, we first propose four types of stochastic efficiencies stochastic expected inefficiency, stochastic expected weak efficiency, stochastic expected efficiency and stochastic expected super-efficiency. We, then, develop three propositions to show the relationship between stochastic efficiency and the expected efficiency. Based on the above research findings, we demonstrate two important properties： （1） The stochastic efficiency is an increase function of the significance level when the expected efficiency remains fixed; （2） The stochastic efficiency is an increase function of the expected efficiency when the significance level remains fixed. Finally, we illustrate the above results by using stochastic simulations and a numerical example.