A beta distribution model for characterizing earthquake damage state distribution

This study investigates methods for modeling the distribution of postearthquake damage among categorical damage states. Specifically, it is demonstrated that the beta distribution is a good model for characterizing the complete probability distribution of damage states conditioned on ground-motion intensity. Based on extensive post-earthquake damage surveys following the 2010 earthquake in Haiti, the paper proposes the method-of-moments and maximum likelihood estimate-based formulations to fit a beta distribution model to grouped categorical damage data. The beta distribution model is further compared with one based on the binomial distribution, often used to estimate damage state distribution. The study demonstrates that the beta distribution results in little bias and variance in predictions of damage and loss. This model can be the basis for developing damage probability matrices, fragility curves, post-disaster damage estimations, risk assessments, and more.