Abstract
A parametric mathematical form of vulnerability function is developed that gives a full probabilistic description of losses as a function of earthquake ground shaking intensity. The model is intended to be used with any loss measure that can take values between 0% and 100%, inclusive, including normalized financial losses (damage ratios), human casualty rates, or debris cover. It is a mixed discrete-continuous probability distribution, in that it assigns a discrete probability mass to experiencing exactly 0% or 100% loss, and a continuous probability density to values in between. The model can be used with empirical or analytical loss data. Two possible regression approaches are presented and Monte Carlo analysis is used to demonstrate that the regressions give unbiased estimates of the model parameters. Finally, the model is applied to a data set of debris cover percentages estimated from detailed finite element analysis of Dutch unreinforced masonry buildings.
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