Direct Quantile Function Estimation Using Information Principles and Its Applications in Reliability Analysis

Abstract

Jaynes's information principle, i.e., maximum entropy principle (MEP), constrained by probability weighted moments (PWM), has been well established as an alternative method to directly estimate quantile functions (QF) from samples of a random variable. The existence, unbiasedness, and efficiency of the maximum entropy QFs have been illustrated in the literature. However, the issue of how many orders of PWMs is optimal for a given sample of data remains unsolved, and applications of the maximum entropy QFs to reliability analysis in civil engineering are still obscure. This paper serves four main purposes: (1) a new general formulation is developed for the PWM-based MEP without sample normalization; (2) the optimal order of PWMs in MEP is determined by another information principle, i.e., Akaike information criterion; (3) The feasibility of the proposed maximum entropy QFs is illustrated by two case studies in probabilistic modeling of the soil undrained shear strength and the flood frequency; (4) applications of the proposed maximum entropy QFs are substantiated in QF-based first order reliability analysis of a cantilever steel beam with uncorrelated random variables and with correlated random variables. The maximum entropy QFs are compared to common empirical probability distributions, such as normal and lognormal distributions, in reliability analysis to demonstrate the advantages and disadvantages of the method developed.