Adaptive Robust Tail Weight (ARTW) Index Revisited: Theory, Implementation, and Applications

The Adaptive Robust Tail Weight (ARTW) index quantifies how heavy or light the tails of a univariate distribution are relative to the Gaussian law while remaining resistant to single‑point outliers. This revision corrects earlier approximations by deriving a full asymptotic variance that accounts for the estimation uncertainty in the median and median absolute deviation (MAD). One‑sided variants are introduced to disentangle asymmetric risks, and the influence of the threshold parameter k is systematically investigated. Extensive Monte‑Carlo experiments compare ARTW with alternative robust kurtosis measures, confirming its superior breakdown point, bounded influence and computational efficiency. Practical guidelines for parameter calibration, block‑bootstrap interval estimation and ready‑to‑use Python/R code snippets facilitate direct deployment in quality engineering and financial risk monitoring applications.