stochastic dea with using of skew-normal distribution in error structure

The stochastic data envelopment analysis (sdea) was developed considering the value of inputs and outputs as random variables. therefore, statistical distributions play an important role in this regard. the skew-normal (sn) distribution is a family of probability density functions that is frequently used in practical situations. in this paper, we assume that the input and output variables are skew-normally distributed. with introducing asymmetric error structure for random variables of sn distribution, a stochastic bcc model is provided. the proposed model includes bcc model assuming a normal distribution of data as well. finally, the proposed model is used in a numerical example.