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

Abstract

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