Hypothesis testing and interval estimation for quantiles of two normal populations with a common mean

The problems of interval estimation of, and testing a hypothesis on the quantile θ=μ+ησ1 (for given η) have been considered when independent random samples are available from two normal populations with a common mean μ and possibly unknown and unequal variances. The asymptotic confidence interval (ACI) for the quantile has been derived using the Fisher information matrix. Further, parametric bootstrap approaches such as boot-p, boot-t as well as the generalized p-value method have been adopted to obtain the confidence intervals numerically. For hypothesis testing several tests such as the one based on the Computational Approach Test (CAT), the likelihood ratio test (LRT), a test using an estimator of quantile, and tests based on generalized p-value approach have been proposed. Finally, the sizes (powers) of all the proposed tests have been computed using Monte-Carlo simulation procedure. Also the confidence intervals have been compared through average length (AL), coverage probability (CP), and a new measure called - the probability coverage density (PCD).