Jackknife empirical likelihood based inference for Probability weighted moments

TL;DR

This paper develops and compares jackknife empirical likelihood methods for constructing confidence intervals and tests for probability weighted moments, demonstrating their effectiveness through theoretical analysis and real rainfall data application.

Contribution

It introduces JEL and AJEL-based inference methods for PWM, providing asymptotic distributions, performance comparisons, and practical testing procedures.

Findings

JEL and AJEL methods achieve accurate coverage probabilities.

Proposed intervals have shorter average length than existing methods.

Application to rainfall data illustrates practical utility.

Abstract

In the present article, we discuss jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) based inference for finding confidence intervals for probability weighted moment (PWM). We obtain the asymptotic distribution of the JEL ratio and AJEL ratio statistics. We compare the performance of the proposed confidence intervals with recently developed methods in terms of coverage probability and average length. We also develop JEL and AJEL based test for PWM and study it properties. Finally we illustrate our method using rainfall data of Indian states.