# Correction to: Improving FEMA P-58 non-structural component fragility functions and loss predictions

• Gemma Cremen
• Jack W. Baker
Correction

## 1 Correction to: Bulletin of Earthquake Engineering  https://doi.org/10.1007/s10518-018-00535-7

Unfortunately, Eqs. 2, 4 and 5 of the associated paper are published incorrectly. We apologize for these errors.

## 2 Equation 2

The likelihood that an arbitrary component is damaged at a level of demand that caused damage ($$edp_i$$) is the normal distribution probability density function (PDF) evaluated at the fragility function defined by Eq. 1, i.e.,
$$\text{Likelihood} = \phi \left( \frac{\ln {(edp_i/\theta )}}{\beta }\right)$$
(2)
where $$\phi (.)$$ is the normal distribution PDF.

Equation 2 should be:

The likelihood that an arbitrary component is damaged at a level of demand that caused damage ($$edp_i$$) is the fragility function defined by Eq. 1, i.e.,
$$\text{Likelihood} = \Phi \left( \frac{\ln {(edp_i/\theta )}}{\beta }\right)$$
(2)

## 3 Equation 4

$$\text{Likelihood} = \left[ \prod _{i=1}^{m}\phi \left( \frac{\ln {(edp_i/\theta )}}{\beta }\right) \right] \left[ 1-\Phi \left( \frac{\ln {(edp_{max}/\theta )}}{\beta }\right) \right] ^{n-m}$$
(4)
Equation 4 should be:
$$\text{Likelihood} = \left[ \prod _{i=1}^{m}\Phi \left( \frac{\ln {(edp_i/\theta )}}{\beta }\right) \right] \left[ 1-\Phi \left( \frac{\ln {(edp_{max}/\theta )}}{\beta }\right) \right] ^{n-m}$$
(4)

## 4 Equation 5

$$\{\hat{\theta }, \hat{\beta }\} = \mathop{{\mathrm{argmax}}}\limits_{\theta ,\beta }\sum _{i=1}^m\left[ \ln \phi \left( \frac{\ln (edp_i/\theta )}{\beta }\right) \right] + [n-m] \ln \left[ 1-\Phi \left( \frac{\ln (edp_{max}/\theta )}{\beta }\right) \right]$$
(5)
Equation 5 should be:
$$\{\hat{\theta }, \hat{\beta }\} = \mathop{{\mathrm{argmax}}}_{\theta ,\beta }\sum _{i=1}^m\left[ \ln \Phi \left( \frac{\ln (edp_i/\theta )}{\beta }\right) \right] + [n-m] \ln \left[ 1-\Phi \left( \frac{\ln (edp_{max}/\theta )}{\beta }\right) \right]$$
(5)