Some quantitative relationships between two types of finite sample breakdown point

The two versions of finite-sample breakdown points, the addition breakdown point and the replacement breakdown point, have been employed in the derivation of the breakdown points for various estimators. However, for a given estimator, frequently only the version that is convenient in the derivation is selected. The connections between the two versions have not yet been formally explored in the literature. In this paper, quantitative relationships between the two versions of the breakdown point are formally established. The result obtained allows one to obtain the ABP directly from the RBP of estimators and vice versa and thus to avoid some unnecessary, sometimes tedious, derivations of breakdown points.