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

M.M. Ali and J. Woo (2008). Inference on reliability P(Y<X) in truncated arcsine distributions. Journal of Statistical Research, Vol. 42, No. 2, pp. 151-158.

Abstract

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 confidence interval for $\rho$ and also provide a test for $\rho.$