IAPO estimators in Exponentiated Frechet case

TL;DR

This paper introduces IAPO estimators for the Exponentiated-Frechet distribution, addressing distribution asymmetry and demonstrating improved tail index estimation through simulations.

Contribution

It extends IAPO estimators to the Exponentiated-Frechet distribution, improving tail index estimation by accounting for asymmetry and simplifying the estimation process.

Findings

IAPO estimators outperform previous IPO estimators in tail index estimation.

Simulation results show favorable convergence rates of IAPO estimators.

IAPO estimators effectively handle distribution asymmetry in tail analysis.

Abstract

In 2017 Jordanova and co-authors consider probabilities for p-outside values, and later on, they use them in order to construct distribution sensitive IPO estimators. These works do not take into account the asymmetry of the distribution. This shortcoming was recently overcome and the corresponding probabilities for asymmetric p-outside values, together with the so-called IAPO estimators, were defined. Here we apply these results to Exponentiated-Frechet distribution, introduced in 2003 by Nadarajah and Kotz. The abbreviation "IAPO" comes from "Inverse Probabilities for Asymmetric P-Outside Values". These estimators use as an auxiliary characteristic the empirical asymmetric $p$-fences. In this way, the system relating the estimated parameters and the asymmetric probabilities for $p$-outside values has an easier solution. The comparison with our previous study about the corresponding IPO and IPO-NM estimators shows that IAPO estimators give better results for the index of regular variation of the right tail of the cumulative distribution function. A simulation study depicts their rates of convergence, and finishes this work.