Advances in computing has undoubtfully been one of the main catalysts in the formation of the discipline always known as Statistics. A fundamental question addressed here is whether computing facilities, such as parallel or high performance computing, could assist in the development of methodologies that render stronger results, based on some predetermined optimality criterion. The candidate at the hand of which this enquiry is made, is the arc length of some statistical function. Estimation, goodness-of-fit, linear regression and non-linear regression, which may all be considered as central themes in Statistics, are revisited, and redefined in terms of this new measure. The results resulting from these arc length methodologies are obtained from simulation, as well as from real case studies, and contrasted to that obtained using their classical counterparts. Mathematical premises for the proposed methods are provided, together with the documentation accompanying the companion R package, along with the data utilised for the applications. / Thesis (PhD)--University of Pretoria, 2017. / National Research Foundation of South Africa, Unique Grant No. 94108. / Statistics / PhD / Unrestricted