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In this paper, copulas and Archimediean copulas (especially with hyperbolic generator) are investigated and it is shown how to use this type of functions in the stochastic frontier analysis. Then we study the efficiency of hydropower plants located on prominent dams in Iran, and based on their performance in 1399 we use data envelopment analysis and stochastic frontier analysis and copulas functions to rank them. In the present study, among the 58 mentioned dams, the dams with an average practical production capacity of at least 10 MW are evaluated. The number of these dams is 29. The calculations show that Gotvand Dam is in the first place and the Mulla Sadra dam has the last rank.