A Gaussian approximation (GA) is commonly used to predict the performance of optical receivers. This is invariably the case if these incorporate superlattice avalanche photo-diodes (SAPDs) since a complete statistical description of the avalanche process associated with these advanced detectors has not been reported when residual hole ionisation is present. The objective of this paper is to present a more rigorous methodology for assessing the performance of these receivers thereby enabling a realistic assessment of the usefulness of the GA to be obtained. A numerical technique based on a discrete ionisation model is used to evaluate the gain moment generating function (MGF) for SAPDs taking into account the influence of both electron and hole ionisation. The MGF of the effective gain associated with detector dark current, generated in the various stages, is also determined using the same approach. This allows us to describe a flexible statistical model for the optical receiver, based on a modified Chenoff bound (MCB), to evaluate the performance of the detection process in the presence of hole ionisation, dark current, and circuit noise. The GA is investigated and compared with MCB calculations. The results indicate clearly that the GA, whilst slightly overestimating the receiver sensitivity (by less than 0.3 dB) and also overestimating the optimum gain, provides a generally good prediction of the opimum threshold and represents a useful basis for initial comparison of the performance of alternative receiver strategies.