High dose rate brachytherapy affords a frequent reassurance of the precise dwell positions of the radiation source. The current investigation proposes a multi-dimensional scaling transformation of both data sets to estimate dwell positions without any external reference. Furthermore, the related distributions of dwell positions are characterized by uni-or bi-modal heavy-tailed distributions. The latter are well represented by α-stable distributions. The newly proposed data analysis provides dwell position deviations with high accuracy, and, furthermore, offers a convenient visualization of the actual shapes of the catheters which guide the radiation source during the treatment.