 finally found a rigorous derivation for the more robust weights, formula_77, as they are defined in the CMA-ES (weights are often zero for ).They are formulated as the consistent estimator for the CDF of formula_161 at the point formula_162, composed with a fixed monotonous decreased transformation formula_163, that is,

This makes the algorithm insensitive to the specific formula_3-values.More concisely, using the CDF estimator of formula_3 instead of formula_3 itself let the algorithm only depend on the ranking of formula_3-values but not on their underlying distribution.