Data envelopment analysis (DEA) measures relative efficiency among the decision making units (DMU) without considering noise in data. The least efficient DMU indicates that it is in the worst situation. In this paper, we measure efficiency of individual DMU whenever it losses the maximum output, and the efficiency of other DMUs is measured in the observed situation. This efficiency is the minimum efficiency of a DMU. The concept of stochastic data envelopment analysis (SDEA) is a DEA method which considers the noise in data which is proposed in this study. Using bounded Pareto distribution, we estimate the DEA efficiency from efficiency interval. Small value of shape parameter can estimate the efficiency more accurately using the Pareto distribution. Rank correlations were estimated between observed efficiencies and minimum efficiency as well as between observed and estimated efficiency. The correlations are indicating the effectiveness of this SDEA model. 1. Introduction Producer performance 1 is influenced by three phenomena: efficiency with which management organizes production, the effect of environmental factors, and random error [1]. If all of these phenomena are influenced positively to production, then it is the best situation for production of the DMU, and if all of these phenomena are influenced the production negatively, then it is the worst situation. Several models of single stage, or multistage have been proposed to incorporate environmental factors in DEA. Banker and Morey [2] proposed a single-stage DEA method for environmental variables. An obstacle of this method is that the direction of impact on production of the environmental factors must be known in advance. In some research, a two-stage approach is used to describe the effect of environmental factors. First stage calculates efficiency from DEA based on inputs and outputs and a second-stage regression analysis tries to explain variation in first-stage efficiency score. A step further, development of the two-stage method was done by McCarty and Yaisawarng [3] and Bhattacharyya et al. [4] by using the second-stage regression residuals to adjust the first-stage efficiency scores. Input oriented DEA to inputs and environmental factors or output oriented DEA to outputs and the environmental factors applied in the first stage. Then, the inputs or outputs were replaced by their residual projections. In the second stage of this method again applied DEA to expanded data set consisting of the originally efficient observations, the originally inefficient observations, and the radial
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