The equations describing diffusion of positrons in krypton and xenon are solved with the best theoretical scattering and annihilation data available to date to obtain the time variation of the positron annihilation rate. The theoretical shoulder lengths obtained with the data of McEachran et al. agree well with the experimental values given by the University College London group, while the shoulder lengths obtained with the data of Schrader are much larger. The present results allow for an assessment of the accuracy of the existent low energy e+Kr and e+Xe elastic cross sections.