Amirkabir University of Technology AUT Journal of Civil Engineering 2588-2899 10 1 2026 02 01 The Appropriate Statistical Distribution for Residuals in Seismic Attenuation Relationships 91 98 5942 10.22060/ajce.2026.24671.5942 EN Shahin Borzoo Department of Civil Engineering, Technical University of Buein Zahra, Buein Zahra, Qazvin, 3451745346, Iran. Journal Article 2025 09 03 The developed ground motion models are mainly based on the assumption of normality of the residuals. The extreme value distribution is a statistical distribution used in modeling rare events and extreme scenarios. In large earthquakes with a long return period, the recorded peak ground accelerations (PGAs) are large and rare, so the assumption of extreme distributions is not unexpected for these accelerations. The extreme value distribution has two conventional forms: generalized extreme value (GEV) for maximum values of blocks with the same time duration and generalized Pareto distribution (GPD) for values above a determined threshold. Due to the lower recorded numbers of PGAs, using the GPD distribution in examining the extreme values ​​of the PGAs is more appropriate. If the GPD distribution assumption for PGA data be accepted, it is suggested to develop a seismic acceleration attenuation relationship for large or extreme data based on the GPD distribution, and the common assumption of lognormal distribution is discarded. This article reviews the statistical distributions used in ground motion models. The results suggest that in the development of ground motion relationships, the normal distribution for residual should be abandoned with a fundamental revision, and the next generation of these models should be developed based on the GPD distribution. https://ajce.aut.ac.ir/article_5942_b0dd033cbe58aa5ea27747271bfd84e3.pdf