Sample-based quantile function estimation using entropy and self-determined probability weighted moments

The method of conventional probability-weighted moments (PWMs) and the principle of minimum cross entropy were combined to derive an analytical form of quantile function [Pandey, 2001]. This method is extended and improved in the present paper by utilizing the concept of self determined probability weighted moments (SD-PWMs). Minimum cross entropy principle and SD-PWMs from sample data were used to evaluate the unknown parameters of the cross entropy quantile function. The performances of the SD-PWM based quantile function were compared with those based on conventional PWMs. The algorithm directly accommodates sample outliers by assigning non-exceedance probabilities accordingly, which is extraordinarily suitable for estimating extreme events from a small sample set. The proposed method would be expected to be used in extreme value and risk analyses of engineering systems.