Exploring the Use of Empirical Distribution Functions in Analyzing Heavy-Tailed and Skewed Data Distributions

Posted: Jan 29, 2015

• Liam Harris
• Isabella Miller
• Owen Lee

Abstract

The analysis of heavy-tailed and skewed data distributions presents significant challenges in statistical computing and data science. Traditional parametric approaches, while computationally efficient, often fail to capture the complex characteristics of modern datasets, particularly those exhibiting extreme skewness and heavy tails. These distributions are increasingly common across diverse domains, including financial markets, network traffic analysis, environmental monitoring, and social network dynamics. The limitations of conventional methods become particularly pronounced when dealing with extreme values and tail behavior, where accurate estimation is crucial for risk assessment and decision-making. Empirical distribution functions (EDFs) offer a nonparametric alternative that avoids strong distributional assumptions. However, standard EDF approaches suffer from several limitations when applied to heavy-tailed and skewed data, including poor performance in tail regions, sensitivity to bandwidth selection, and computational inefficiency with large datasets. This research addresses these challenges by developing an enhanced EDF framework that incorporates adaptive bandwidth selection, tail regularization, and computational optimization techniques. Our work makes several key contributions to the field of statistical computing. First, we introduce a multi-scale bandwidth selection algorithm that dynamically adapts to local density variations while maintaining statistical consistency. Second, we develop a tail regularization technique that stabilizes extreme value estimation without imposing parametric assumptions. Third, we propose a computational framework that enables efficient implementation on large-scale datasets through parallel processing and memory optimization.