 the values of $\underline{R}_{{\mathcal{C}},j}$, $\bar{r}_{{\mathcal{C}},j}  ({\boldsymbol{\theta}},{\boldsymbol{\theta}}')$ and $\underline{{r}}_{{\mathcal{C}},j}  ({\boldsymbol{\theta}},{\boldsymbol{\theta}}')$ 