This result is applied in order to develop a powerful nonparametric EL ratio test and the corresponding distribution-free confidence interval (CI) estimation of the PWMs.
We show that the proposed method can be easily applied towards inference of the Gini index, a widely used measure for assessing distributional inequality.
An extensive Monte Carlo (MC) study shows that the proposed technique provides a well-controlled Type I error rate, as well as very accurate CI estimation, that outperforms the CI estimation based on the classical schemes to analyze the PWMs.
These results are clearly observed in the cases when underlying data are skewed and/or consist of a relatively small number of data points.
A real data example of myocardial infarction disease is used to illustrate the applicability of the proposed method.