TCM, TKSCM and TCMKS. Here, TKS and TCM refer to Kolmogorov-Smirnov and Cramér-von Mises distances respectively, while TKSCM and TCMKS are mixtures of both. For simplicity, the weight functions are chosen identically equal to $1$ in all the settings, i.e., $w(y,s) =1$ for all $ (y,s) \in \mathbb{R} \times [0,1] $, $w(y)=1$ for all $y \in \mathbb{R}$ and $w(s)=1$ for all $s \in [0,1]$ in $(ii)$, $(iii)$ and $(iv)$, respectively (although for the theory we assumed a compact support). We sum up the simulation results in the following 8 tables. Tables \[Table1\], \[Table7\] and Tables \[Table2\], \[Table8\] deal with Models and for $a_n=b_n/2$ and $a_n=b_n/20$, respectively, whereas Tables \[Table3\], \[Table5\] and Tables \[Table4\], \[Table6\] in the supplement show the results for Models and . In Figure \[est\], we have represented the density function of each estimator for the Model when $\t_0=0.5$ with $n=100$ and $a_n=b_n/20$, which corresponds to the settings of Table \[Table2\]. To assess the performance of our estimates, we provide for each estimator the mean, the median and the Mean Integrated Squared Error (MISE) in brackets for five values of the true parameter $\t_0=0,0.5,1,1.5,2$. The best-performing one regarding the mean (respectively the MISE) is highlighted in bold (respectively 