this paper addresses the problem of testing simple hypotheses about the mean of a bivariate normal distribution with identity covariance matrix against restricted alternatives. the lrts and their power functions for such types of hypotheses are derived. furthermore, through some elementary calculus, it is shown that the power function of the lrt satisfies certain monotonicity and symmetry prope...

One way to characterize and understand H I-selected galaxies is to study their metallicity properties. In particular, we show that the metallicity of absorbers is a bivariate function of the H I column density (NH I) and the Mg II equivalent width (W λ2796 r ). Thus, a selection upon W r is not equivalent to a H I selection for intervening absorbers. A direct consequence for damped absorbers wi...