Abstract
Given realizations of two possion processes with unknown intensities A(·) and F(·) observed over the interval (t1,t2), we suppose that it is desired to distinution between H0 Ξ(·)/λ(·) is constant on (t1,t2) versus H+:Ξ(·)/λ(·) increases on (t1,t2). We propose a decision rule which uses the percentage points of the Mann-Whitney U-distribution. We show that the decision rule is unbiased and that the set of alternatives in H+ can be weakly ordered, specifically: if Ξ(·)/λ(·), β(·)/λ(·) and Ξ(·)/β(·) are increasing on (t1, t2) then P{H0 is rejected |Ξ(·)}≧P{H0 is rejected|B(·)}≧P{H0 is rejected|H0}.