Before revision:  In order to demonstrate a strength of the optimality of the bin-width we compare the  \delta-spectrum for various bin-widths . Implications for the multifractal \delta-spectrum as a function of Renyi 's q parameter are also discussed and graphically represented .
After revision:  In order to demonstrate a strength of the optimality of the bin-width we compare the \delta-spectrum for various bin-widths and show the robustness of the method, especially for large values of q. For such values, other methods in use, e.g., those based on moment estimation, tend to fail for heavy-tailed data or data with long correlations. Connection between the \delta-spectrum as a function of Renyi 's q parameter are also discussed and graphically represented .