Inference on reliability P(X<Y) in truncated arcsine distributions

We consider inference on reliability R = P(Y <X), where the random variables
X and Y are independent truncated arcsine distributions with parameters \beta_1 and
\beta_2, respectively. We obtain the maximum likelihood estimator of R in terms of
\rho=\beta-1/\beta_2 and observe that inference on R is equivalent to inference on \rho, where
R is a monotone function of \rho. We obtain an exact and an approximate con dence
interval for \rho and also provide a test for \rho.