The Appropriate Statistical Distribution for Residuals in Seismic Attenuation Relationships

Document Type : Review Article

Author

Civil Engineering Department, Technical University of Buein Zahra, Buein Zahra, Qazvin, 3451745346, Iran

Abstract

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 less 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 critical 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 suggests that in the development of ground motion relationships, the normal distribution for residual be abandoned with a fundamental revision and the next generation of these models should be developed based on the GPD distribution.

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AUT Journal of Civil Engineering
Volume 10, Issue 1
in progress
February 2026

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