Comparing the Efficiency of Dmus with Normal and Skew-Normal Distribution using Data Envelopment Analysis

Data envelopment analysis (DEA) is a nonparametric approach to evaluate the efficiency of decision making units (DMU) using mathematical programming techniques. Almost, all of the previous researches in stochastic DEA have been used the stochastic data when the inputs and outputs are normally distributed. But, this assumption may not be true in practice. Therefore, using a normal distribution will be lead to wrong results. The skew-normal (SN) distribution is one of the important distribution in statistics. The SN distribution is an asymmetric distribution which has similar properties to a normal distribution and it can be extended to the normal distributions. In the present study, a stochastic BCC model was proposed for measuring the stochastic efficiency of DMUs with inputs and outputs having Skew- Normal (SN) distribution. Moreover, it is shown that this model encompasses the BCC model assuming the normality of data as well. The proposed model in measuring the efficiency of a bank's 25 branches is used.