Use of transform pairs to represent and simulate nonstationary non-Gaussian process with applications

•Emphasize a new concept to represent nonstationary non-Gaussian process using transform pairs.•Use the iterative power and amplitude correction (IPAC) algorithm with different transform pairs.•Propose a modified version of the IPAC algorithm for nonstationary non-Gaussian process (NNP)•Compare the performance of the IPAC algorithm and spectral representation method to simulate NNP.•Apply the IPAC algorithm to estimate structural reliability for a catalogue of seismic events.