ABSTRACT
Probability weighted moments (PWMs) are considered to be a generalization of the conventional moments of a probability distribution incorporating the distribution function in their expectation. PWM-based techniques provide favorable estimation properties when using samples with relatively small sizes and are computationally straightforward to calculate. This chapter discusses a general scheme to construct empirical likelihood (EL) inference of the PWMs. Main task consists of forming constraints relevant to PMWs and showing that the developed EL test follows the classical asymptotic theories. The statistical test and CI estimation of the PWMs are derived based on the asymptotic proposition. PMW EL ratio method is applied to make inference of the Gini index. Relevant R codes for practitioners are provided.
