Characterization based Goodness-of-Fit for Generalized Pareto Distribution: A Blend of Stein's Identity and Dynamic Survival Extropy

TL;DR

This paper introduces a new goodness-of-fit test for the generalized Pareto distribution using Stein's identity and dynamic survival extropy, applicable to both positive and negative shape parameters, with demonstrated effectiveness through simulations and real data.

Contribution

It presents a novel goodness-of-fit test for GPD based on new characterizations, including for censored data, with proven asymptotic properties and high power.

Findings

Test has high power against various alternatives.

Applicable to censored data with a provided procedure.

Demonstrated effectiveness through simulations and real-world applications.

Abstract

This paper proposes a goodness of fit test for the generalized Pareto distribution (GPD). Firstly, we provide two characterizations of GPD based on Stein's identity and dynamic survival extropy. These characterizations are used to test GPD separately for the positive and negative shape parameter cases. A Monte Carlo simulation is conducted to provide the critical values and power of the proposed test against a good number of alternatives. Our test is simple to use and it has asymptotic normality and relatively high power, which strengthened the purpose of proposing it. Considering the case of right censored data, we provide the procedure to handle censored case too. A few real-life applications are also included.