Science and Education Publishing American Journal of Applied Mathematics and Statistics 2333-4576 2 3 2014 05 03 Inference on P(X < Y) for Extreme Values 121 128 EN Sudhansu S. Maiti Department of Statistics, Visva-Bharati University Santiniketan, India Sudhir Murmu AJAMS2014236 10.12691/ajams-2-3-6 2014 04 12 2014 04 24 2014 05 03 The article considers the problem of , when X and Y belong to independently distributed two extreme value distributions. Maximum likelihood estimate of R has been found out and the estimates assuming different distributions have been compared for complete samples. Lower confidence limits of R have been found out by Delta method and bootstrap method. The Bayes estimate of R has also been calculated using MCMC approach.