Correction to: Test (2011) 20: 180–203 https://doi.org/10.1007/s11749-010-0193-3

In the first expression in Section 5 the factor \(1/(2\pi )\) is missing; this expression should rather read

$$\begin{aligned} \Delta =\frac{1}{2\pi }\int _{-\infty }^{+\infty }\left| \frac{\Phi _{W_k}(t)-\Phi ^*_{W_k}(t)}{t}\right| dt \end{aligned}$$

Also in Section 5, right befor the first expression in the second paragraph, where it is written \(W=W_k+W_{k'}\), it should be mentioned ‘where \(W_k\) and \(W_{k'}\) are independent’. And yet on this same paragraph, in expression (30), the factor \(1/(2\pi )\) is missing in all expressions, and there is also a \(W_2\) which should be \(W_{k'}\); this expression should rather read

$$\begin{aligned} \displaystyle \Delta _W= & {} \displaystyle \frac{1}{2\pi }\int _{-\infty }^{+\infty }\left| \frac{\Phi _W(t)-\Phi ^*_{W}(t)}{t}\right| dt\nonumber \\= & {} \displaystyle \frac{1}{2\pi }\int _{-\infty }^{+\infty }\left| \frac{\Phi _{W_k}(t)\Phi _{W_{k'}}(t)-\Phi _{W_k}(t)\Phi ^*_{W_{k'}}(t)}{t}\right| dt\nonumber \\= & {} \displaystyle \frac{1}{2\pi }\int _{-\infty }^{+\infty }\underbrace{\left| \Phi _{W_k}(t)\right| }_{\le 1}~\left| \frac{\Phi _{W_{k'}}(t)-\Phi ^*_{W_{k'}}(t)}{t}\right| dt\nonumber \\\le & {} \displaystyle \frac{1}{2\pi }\int _{-\infty }^{+\infty }\left| \frac{\Phi _{W_{k'}}(t)-\Phi ^*_{W_{k'}}(t)}{t}\right| dt\,=\,\Delta _{W_{k'}}. \end{aligned}$$
(30)