Optimal Maximum Entropy Quantile Function for Fractional Probability Weighted Moments and Its Applications in Reliability Analysis

The maximum entropy principle (MEP) under the constraint of fractional probability weighted moments (FPWM) is a well-developed method for a direct estimation of the quantile function of a random variable. The accuracy, unbiasedness, and efficiency of maximum entropy quantile functions (MEQFs) have been demonstrated in the literature. However, the issue of how to select an optimal order of FPWMs given a sample of data is not fully solved, and the application of this approach to reliability analysis in civil engineering has not been fully investigated. This paper presents a FPWM-based MEP with a new nondimensional analysis and proposes the Akaike information criterion to determine the optimal order of FPWM in MEP analysis. To illustrate this approach, two examples of the estimation of optimal quantile functions for soil undrained shear strength and annual maximum daily discharge are presented. The paper presents a novel approach to use the quantile function for the First Order Reliability Method, a widely used method in civil engineering. As a case study of this approach, the reliability analysis of a rock slope is included. The FPWM-based MEQFs are compared with common empirical distributions and MEQFs based on integral probability weighted moments to demonstrate the advantages and disadvantages of the developed method.