Võrdle meetodeid

	Vulnerability and Damage Function Analysis	Average Annual Loss Estimation
Valdkond	Disaster Studies	Disaster Studies
Perekond	Process / pipeline	Process / pipeline
Tekkeaasta	2003	2005
Looja	Tiziana Rossetto & Amr Elnashai; Charles Kircher, Robert Whitman & William Holmes	Patricia Grossi & Howard Kunreuther; Vitor Silva et al. (GEM)
Tüüp	Loss-ratio estimation pipeline conditional on hazard intensity	Expected-value risk metric computed from a loss exceedance distribution
Algallikas	Rossetto, T., & Elnashai, A. (2003). Derivation of vulnerability functions for European-type RC structures based on observational data. Engineering Structures, 25(10), 1241-1263.	Grossi, P., & Kunreuther, H. (Eds.) (2005). Catastrophe Modeling: A New Approach to Managing Risk. Springer. ISBN: 9780387241050
Rööpnimetused	Damage Function Estimation, Loss Ratio Curves, Mean Damage Ratio Functions, Stage-Damage Functions	Annual Average Loss (AAL), Annualized Expected Loss, Pure Premium Estimation, Expected Annual Damage
Seotud	4	4
Kokkuvõte	Vulnerability and damage function analysis estimates the expected loss ratio, the repair or replacement cost expressed as a fraction of an asset's value, as a continuous function of hazard intensity. It is the loss-facing counterpart to fragility analysis: where fragility gives the probability of physical damage states, a vulnerability function gives money, translating intensity directly into expected fractional loss together with its uncertainty. Tiziana Rossetto and Amr Elnashai's 2003 derivation of vulnerability functions for European reinforced-concrete buildings from observed damage is a canonical empirical example, while Charles Kircher, Robert Whitman, and William Holmes's 2006 description of HAZUS earthquake methods shows the standard route of combining fragility curves with damage-state loss factors to build them analytically. The output is the per-typology relationship that, multiplied by exposed value, yields scenario and probabilistic loss. Because it bridges engineering damage and economic consequence, it is the single most influential ingredient in catastrophe and loss models. Getting the mean and the spread of the loss ratio right is what makes a risk model usable for insurance, mitigation, and policy.	Average annual loss (AAL) estimation computes the expected loss per year from a hazard, the long-run mean of annual losses obtained by weighting every possible event's loss by its annual frequency. It is the single most important summary statistic produced by probabilistic risk and catastrophe models, equal both to the frequency-weighted sum of event losses and to the area under the loss exceedance curve. Patricia Grossi and Howard Kunreuther's 2005 volume sets out how AAL and the exceedance curve are derived and used in risk management, and Vitor Silva and colleagues' 2020 global seismic risk model reports AAL (and AAL ratios) as its headline risk metric across the world. Because it is an expected value, AAL is additive across assets, perils, and regions, which makes it ideal for ranking risk, setting the technical (pure) insurance premium, and screening mitigation. Unlike return-period losses it says nothing about the tail, so it is the complement to probable maximum loss rather than a substitute. Estimating it correctly means handling both frequencies and the full range of event losses, including rare severe ones.