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.

对数正态分布是许多不同概率地震评估（例如地震危险性分析，脆弱性分析和可靠性评估）中最适用的分布之一。这项研究比较了样本中位数（SM），样本几何平均值（SGM）和样本偏差校正几何平均值（SBCGM）作为对数正态中心估计量的三个不同估计量，它们来自不同方面。为此，使用蒙特卡洛模拟通过计算其偏差和最小平方误差（MSE）来研究每个估计器的效率。此外，使用增量动力分析（IDA）研究了四个钢制抗弯框架（SMRF）的概率性能，并考虑了不确定性和认识论上的不确定性，研究了其中一个（5层框架）的随机抗震性能。另外，根据IDA程序对数正态集中趋势的统计估计量，研究了基于上述外套套型海上平台的概率地震性能。结果表明，SM的效率明显低于其他两个估计器。通常，对于小样本量而言，SBCGM是最有效的一种。但是，随着样本量的增加，SBCGM和SGM表现出相同的效率。同样，基于每个估计量，可以观察到结构在地震性能方面的明显差异。根据拟合检验的良好程度和似然比评估的结果，建议使用SBCGM以在使用少量记录时实现更可靠的地震评估。作为另一个边缘结论，