What is Order Statistics

A criticism leveled against Data Envelopment Analysis (DEA) is that it is incapable of handling input/output data contaminated with random errors, and therefore, efficiency scores reported by DEA do not reflect reality. Several researchers have addressed this issue by incorporating statistical noise into DEA modeling, thus giving birth to Stochastic DEA. In this chapter, utilizing well known DEA models, we propose a method to randomize efficiency scores by treating each score as an order statistic of an underlying Beta distribution. In an application to a set of banks, we demonstrate how to do this randomization and derive some statistical results.