A class of order statistic filters consisting of linear combinations of moving quasiranges has been proposed for the detection of edges in images [Restrepo et al., 1994]. Here, the distributions of quasiranges are obtained, for samples containing several outliers, and used to compute statistics such as expectations, variances and probabilities of error of the corresponding quasirange. A procedure for the choice of the threshold level is given; such a threshold level determines a minimal edge contrast to be detected under acceptable SNR conditions. We give several examples for the case of window size five.