Nonlinear dynamic analysis is often used to develop fragility curves within the framework of seismic risk assessment and performance-based earthquake engineering. In the present article, fragility curves are derived from randomly generated clouds of structural response results by using least squares and sum-of-squares regression, and maximum likelihood estimation. Different statistical measures are used to estimate the quality of fragility functions derived by considering varying numbers of ground motions. Graphs are proposed that can be used as guidance regarding the number of calculations required for these three approaches. The effectiveness of the results is demonstrated by their application to a structural model. The results show that the least-squares method for deriving fragility functions converges much faster than the maximum likelihood and sum-of-squares approaches. With the least-squares approach, a few dozen records might be sufficient to obtain satisfactory estimates, whereas using the maximum likelihood approach may require several times more calculations to attain the same accuracy.
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