A direct method of the computation of the oc and of the moments of the sample number for sprts in the case of discrete-random variables

Abstract

Let X 1,X 2, … be a sequence of independent and identically distributed ran-dom variables with the density f(x,θ) with respect to a measure on the set of integer numbers. We suppose that . holds for any given . If u(θ0, θ1)/v(θ0, θ1) is a rational number we reduce the problem of the computation of the OC and the moments of the sample number of an SPRT for H0:θ=θ0 against H1:θ=θ1 to that of solving of systems of simultaneous linear equa-tions which only differ in their right sides, By means of these systems of simultaneous linear equations we may also compute the OC and the moments of the sample number' of truncated SPRTs. For this end we have to solve the considered systems of simul-taneous linear equations by the method of iteration using suitable chosen initial conditions.