Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 1 1 2013 07 04 Stochastic DEA with a Perfect Object and Its Application to Analysis of Environmental Efficiency 57 63 EN Alexander Y. Vaninsky Mathematics Department, City University of New York/Hostos Community College, New York, USA AJAMS2013142 10.12691/ajams-1-4-2 2013 01 17 2013 07 03 2013 07 04 The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distribution of the efficiency score, to find its mathematical expectation, and to deliver common (group¨Crelated) and partial (object-related) efficiency components. We apply this approach to a prospective analysis of environmental efficiency of the major national and regional economies.