Average case analysis forms an interesting and intriguing part of algorithm theory since it explains why some algorithms with bad worst-case complexity can be better on the average. Famous examples are the quicksort, simplex method and the wide variety of computer graphics and computational geometry algorithms. Here we make a statistical case study on the robustness of average complexity measures, which are derived assuming uniform distribution, for non-uniform inputs (both discrete and continuous). (Authorâ€™s abstract)