A general discussion is presented of the problems involved in estimating the Circular Probable Error CEP. A comparison is made between the estimates of the CEP under two distinct models. The models are identical except for the location of the mean vector in relation to the target. The assumption of dependence is made in both models and the resulting estimates are compared with the corresponding estimates obtained under the assumption of independence. Confidence interval estimates of the CEP are also presented. Two methods of removing outlier or Maverick observations are introduced and some of the possible effects on the estimated CEP are discussed. The different estimating procedures are illustrated with three numerical problems.