The importance and applications of sorting is apparent and needs no explanation. In this paper, we analyse a non-comparison sorting algorithm, Base-n Radix Sort (BNRS) and introduce an optimized vari- ant of BNRS, namely, Stable Logical Partition Radix Sort (SLPR). The complexity of these algorithms is measured by the input size $n$ and the maximum value $k$. We show that with respect to time complexity, these algorithms are more succinct than traditional comparison-based sorting algorithms for representing the sorted order of certain integer distribu- tions, specifically, when $k