Comparing the Efficiency of Dmus with Normal and Skew-Normal Distribution using Data Envelopment Analysis
Subject Areas : Statistics
1 - Department of Statistics, Science and Research Branch, Islamic Azad University,
Tehran, Iran
2 - Department of Statistics, Science and Research Branch, Islamic Azad University,
Tehran, Iran
Keywords: تحلیل پوششی دادهها, برنامهریزی درجه دوم, توزیع چوله- نرمال, توزیع چوله نرمال بسته,
Abstract :
Data envelopment analysis (DEA) is a nonparametric approach to evaluate theefficiency of decision making units (DMU) using mathematical programmingtechniques. Almost, all of the previous researches in stochastic DEA have been usedthe stochastic data when the inputs and outputs are normally distributed. But, thisassumption may not be true in practice. Therefore, using a normal distribution willbe lead to wrong results. The skew-normal (SN) distribution is one of the importantdistribution in statistics. The SN distribution is an asymmetric distribution which hassimilar properties to a normal distribution and it can be extended to the normaldistributions. In the present study, a stochastic BCC model was proposed formeasuring the stochastic efficiency of DMUs with inputs and outputs having Skew-Normal (SN) distribution. Moreover, it is shown that this model encompasses theBCC model assuming the normality of data as well. The proposed model inmeasuring the efficiency of a bank's 25 branches is used.
