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

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 the QFs have illustrated in literature. However, issue how many orders PWMs is optimal for given sample data remains unsolved, applications reliability analysis civil engineering are still obscure. This paper serves four main purposes: (1) new general formulation developed PWM-based MEP without normalization; (2) order determined another Akaike criterion; (3) feasibility proposed two case studies probabilistic modeling soil undrained shear strength flood frequency; (4) substantiated QF-based first cantilever steel beam with uncorrelated variables correlated variables. compared common empirical distributions, such normal lognormal demonstrate advantages disadvantages developed.