AbstractIn this paper, an adaptive Hermite distribution model with probability-weighted moments (PWMs) is proposed for evaluating the extreme-value distribution (EVD) of response, which serves as the basis of seismic reliability analysis of complex nonlinear structures under random seismic excitations. From the perspective of EVD, the problem formulation is first introduced. Then, an adaptive distribution model, named as the adaptive Hermite polynomial normal transformation model (A-HPNT), is established to estimate the EVD. The undetermined coefficients of A-HPNT are specified via the PWMs matching technique, in which only linear systems of equations need to be solved. To optimally determine the degree for A-HPNT, a two-step criterion is effectively established accordingly. An efficient high-dimensional sampling technique is introduced for generating samples of extreme value, estimating both the PWMs and statistical moments of EVD. When the entire distribution of EVD is recovered, one can compute the failure probability and reliability index via an integral over the EVD. Two numerical examples, a 10-story nonlinear shear frame structure and a practical 13-story reinforced concrete frame-shear wall structure driven by random seismic excitations, are presented to verify the efficacy of the proposed method for seismic reliability evaluation of complex nonlinear structures.