Tests on the intensity of a poisson process
John G. Saw · Communications in Statistics · 1975
Given a realization of a Poisson process of unknown intensity λ(u) observed over the interval (t1,t2) and for a given function p(u) positive on (t1,t2) we suppose that it is desired to distinguish between Ho λ(u)/ρ(u) is constant on (t1,t2) versus H+: λ(u)/ρ(u) increases on (t1,t2). We propose a decision rule which uses the percentage points of the chi-squared distribution We show that the decision rule is unbiased and that the set of alternatives in H+ can be weakly ordered, specifically: if α(u)/ρ(u), β(u)/o(u), α(u)/β(u) increase on (t1,t2) then P{Ho is rejected∣α( )}>P{Ho is rejected∣s( )} > P{Ho is rejected∣Ho}.