Distribution-Aware Outlier Detection in High Dimensions: A Scalable Parametric Approach

We propose a distribution-aware framework for unsupervised outlier detection that transforms multivariate data into one-dimensional neighborhood statistics and identifies anomalies through fitted parametric distributions. This directly addresses central difficulties of high-dimensional data—including sparsity of observations, the concentration of pairwise distances, hubness phenomena in nearest-neighbor graphs, and general effects of the curse of dimensionality that degrade classical distance-based scoring. Supported by the Cumulative Distribution Function (CDF) Superiority Theorem and validated through Monte Carlo simulations, the method connects distributional modeling with Receiver Operating Characteristic–Area Under the Curve (ROC–AUC) consistency and produces interpretable, probabilistically calibrated scores. Across 23 real-world datasets, the proposed parametric models demonstrate competitive or superior detection accuracy with strong stability and minimal tuning compared with baseline non-parametric approaches. The framework is computationally lightweight and robust across diverse domains, offering clear probabilistic interpretability and substantially lower computational cost than conventional non-parametric detectors. These findings establish a principled and scalable approach to outlier detection, showing that statistical modeling of neighborhood distances can achieve high accuracy, transparency, and efficiency within a unified parametric framework.