Rankiniu

Rankiniu is a term used in statistical discourse to describe a family of indices that quantify how stable a ranking of items remains under perturbations to the underlying data. The concept addresses the robustness of an observed ranking in the presence of measurement error, sampling variability, or noise, and is used to compare the resilience of different rankings under defined disturbance models.

In its typical formulation, Rankiniu is defined for a baseline ranking of n items. A perturbation model is specified for the data, such as additive noise drawn from a chosen distribution. The Rankiniu value is the expected fraction of item pairs whose relative order agrees between the baseline ranking and a perturbed ranking, averaged over the perturbations. Equivalently, it can be viewed as the probability that a random pair maintains its order; the value lies between 0 and 1, with higher values indicating more stable rankings.

Variants exist that modify how pairwise agreements are counted, producing Kendall-like and Spearman-like implementations. Rankiniu_K emphasizes concordance of pairwise orders, while Rankiniu_S emphasizes rank-distance compatibility between original and perturbed rankings. Both variants aim to capture the same general notion of robustness under noise.

Applications of Rankiniu include evaluation of ranking systems in information retrieval, sports analytics, finance, and recommender systems. In practice, the choice of perturbation model influences the resulting Rankiniu value, so it is most informative when used to compare stability under identical noise assumptions. Limitations include model-dependence and the fact that a single stability score does not reveal which items are responsible for instability.

See also Kendall tau, Spearman's rho, rank correlation, and robust statistics.