Probabilistic assessment of earthquake insurance rates for buildings - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 785

ship, respectively. Moreover, stochastic models corresponding to differ-
ent combinations of these alternatives should be developed. In the
estimation of the parameters a and b of Gutenberg-Richter's magni-
tude-frequency relationship, the modifi ed maximum likelihood (MML)
method should be preferred. The MML estimators are more precise and
robust, compared to the least squares (LS) and maximum likelihood
(ML) estimators, especially when the error distribution is non-normal
(Yucemen and Akkaya, 2012).
5. An adequate set of intensity attenuation equations is developed and/or
selected.
6. Preparation of a computational algorithm which aggregates the seismic
threat nucleating from different sources, yielding the probability distri-
bution for the earthquake intensity at a specifi ed location. Generally, a
series of computer programs are utilized to perform the necessary
computations.
7. To account for alternative assumptions and data/parametric/model
uncertainties, different sources of uncertainties (aleatory and epistemic)
are characterized and incorporated either directly in the hazard calcula-
tions or by conducting sensitivity studies through logic tree or statistical
methods.

8. Seismic hazard curves are developed by computing exceedance prob-

abilities for different earthquake intensity levels.

29.2.2 Estimation of potential earthquake damage

The other component of the probabilistic model involves the assessment of
seismic vulnerability of buildings. Damage is commonly described by a loss
ratio that varies with the strength of shaking and type of structure (Whitman,
1973; Blong, 2003a; Askan and Yucemen, 2010). Due to uncertainties
involved, damage that may occur during future earthquakes should be
treated in a probabilistic manner.
The most reliable data source for earthquake damage estimation is the
observed damage data, provided that personal bias in the damage evalu-
ation is eliminated. However, when there is lack of adequate data, missing
or unreliable parts of the available data can be complemented based on
analytical methods and/or expert opinion.
The expected earthquake damage can be presented in various ways. In
the current study, the damage probability matrix (DPM) proposed by
Whitman (1973) is adopted. This is based on the facts that many past studies
used this method consistently (e.g. Steinbrugge, 1982; Yucemen, 2005). Note
that the damage probability matrix approach facilitates the conversion of
the observed damage data into a probabilistic format. The general form of
a DPM is shown in Table 29.1.