A statistical study on lognormal central tendency estimation in probabilistic seismic assessments

Lognormal distribution is one of the most applicable distributions in many different probabilistic seismic assessments such as seismic hazard analysis, fragility analyses, and reliability evaluations. This study compares the sample median (SM), sample geometric mean (SGM) and Sample Bias Corrected Geometric Mean (SBCGM) as three different estimators of lognormal central estimator from different aspects. To this end, the efficiency of each estimator is investigated by calculating their bias and minimum squared error (MSE) using Monte Carlo Simulations. Further, probabilistic performance of four Steel Moment Resisting Frames (SMRF) is investigated using Incremental Dynamic Analysis (IDA), and the stochastic seismic performance of one of them (5 story frame) is investigated considering the aleatoric and epistemic uncertainties. Additionally, the probabilistic seismic performance of a sample jacket type offshore platform based on the mentioned statistical estimators of lognormal central tendency is investigated implementing the IDA procedure. The results show that the efficiency of SM is significantly lower than the other two estimators. In general, SBCGM is the most efficient one for small sample sizes. However, SBCGM and SGM show the same efficiency as the sample size increases. Also, noticeable differences can be observed in the seismic performance of the structures based on each estimator. According to the results of goodness of fit tests and the likelihood ratio evaluations, SBCGM is recommended for achieving more reliable seismic assessments when using small number of records. As another marginal conclusion, the conducted statistical study revealed that the lognormal assumption is approved for collapse fragility curves considering both aleatoric and epistemic sources of uncertainty.