Estimating the Statistical Anomaly of the Underlying Point Process—The Proper Approach to Yarn Irregularity

Abstract

This paper, which is based on the Martindale-Giesekus yarn model, points out recent advances in research on point processes, extends them where necessary, and so provides a solution to the problem of estimating the statistical anomaly of the underlying point process of fiber end points. It is argued that estimating the anomaly (a function) is the natural extension and refinement to estimating Huberty's κ (a constant), and therefore the proper method of measuring yarn irregularity. The estimators of 1 — κ are in fact estimators of the anomaly at argument zero.