A mixture model for unsupervised tail estimation

TL;DR

This paper introduces an unsupervised mixture model that combines multiple densities to effectively estimate tails of distributions, adaptable to both heavy and light tails, with smooth density estimation via cdf functions.

Contribution

It presents a novel unsupervised approach using cdf-based mixing for tail estimation, allowing flexible modeling of diverse tail behaviors.

Findings

Compared with existing models, showing improved tail estimation accuracy

Demonstrated the method's effectiveness on various distributions

Achieved smooth density estimates with simultaneous parameter and threshold estimation

Abstract

This paper proposes a new method to combine several densities such that each density dominates a separate part of a joint distribution. The method is fully unsupervised, i.e. the parameters in the densities and the thresholds are simultaneously estimated. The approach uses cdf functions in the mixing. This makes it easy to estimate parameters and the resulting density is smooth. Our method may be used both when the tails are heavier and lighter than the rest of the distribution. The presented model is compared with other published models and a very simple model using a univariate transformation.