Performance of sorting algorithms on data generated using various statistical distributions: A comprehensive study of sorting techniques

Abstract

Sorting numbers, objects, or living things is of immense importance in most scientific fields. It is of great importance in physics, computer science, statistics, and nanoparticle dynamics. This study presents a comparative evaluation of seven sorting algorithms: Merge, Heap, Quick, Bubble, Insertion, Radix, and Shell Sort, using datasets generated from nine statistical distributions, namely Normal, Uniform, Poisson, Gumbel, Laplace, Weibull, Exponential, Chi-Square, and Binomial. Algorithm performance is analyzed based on the execution time required to sort datasets under varying statistical conditions. The results confirm that input distribution strongly affects sorting efficiency. Bubble Sort and Insertion Sort consistently exhibited the longest execution times, highlighting their poor scalability for large datasets. Merge Sort and Heap Sort show stable and robust performance across all distributions, making them dependable general-purpose choices. Quick Sort and Shell Sort are most effective for symmetric datasets but show moderate sensitivity to skewed and heavy-tailed inputs. Radix Sort remains highly efficient for integer data, though wider value ranges increase computational cost. Overall, the findings highlight that optimal sorting performance depends on matching the algorithm to the statistical characteristics of the input data