Transformed jackknife empirical likelihood for probability weighted moments

Abstract

Probability weighted moments (PWMs) are a generalization of the usual moments of a probability distribution. In this paper, the jackknife empirical likelihood (JEL), the adjusted JEL (AJEL), the transformed JEL, which combines the merits of jackknife and transformed empirical likelihoods (TJEL), the transformed adjusted JEL (TAJEL), the mean jackknife empirical likelihood (MJEL), the mean adjusted jackknife empirical likelihood (MAJEL), and the adjusted mean jackknife empirical likelihood (AMJEL) methods, are considered to construct confidence intervals for probability weighted moments. Simulation results under various distributions show that MAJEL method always gives the best performance in terms of the coverage probability and average length among these methods, and TJEL shows better performance than AJEL and MJEL for small sample sizes, while MJEL is relatively time-consuming. The tests based on the proposed methods for PWMs are also developed. Real datasets are used to illustrate the proposed procedures.