## 1 Introduction  
Loss estimation in buildings due to earthquake shaking is critical for performance-based earthquake engineering (PBEE), which comprises four major components--seismic hazard, building response, probability of damage, and the costs due to losses and repairs. The engineering decisions on the retrofitting of structures are made based on probabilistic estimates of seismic performance of structures in terms of repair cost, casualties, and loss of functionality acceptable to stakeholders. In the first two stages of the PBEE framework, seismic hazard and building responses are estimated and represented in terms of \"intensity measures\" (IMs) and \"engineering demand parameters\" (EDPs). The implementation of a PBEE framework relies strongly on the ability of IMs to predict EDPs accurately. Each stage of PBEE is accompanied by uncertainties, both seismological and structural, influencing loss estimation [1]. Limited knowledge about earthquake source processes, Earth structure, and local site conditions contribute to uncertainties in seismological parameters, which in turn influence the estimation of IMs. Empirical ground motion prediction equations (GMPEs; also called ground motion models, GMMs) are available to predict IMs [2]. In GMMs, the complexities of the earthquake source process and seismic wave propagation in 3D heterogeneous Earth are simplified and then statistically accounted for when estimating ground motion intensities for future earthquakes. In addition to the seismological uncertainties, uncertaintiesin the structural response of buildings play a significant role in PBEE. These include the uncertainties in the estimation of stiffness, damping, and inertial characteristics of the building frame. The characteristics of earthquake ground motion can be described by several types of IMs, related to the amplitude, frequency, and energy of ground motion. Therefore, to establish a meaningful relationship between ground motion and the corresponding structural response, it is necessary to investigate a broad range of IMs and analyze their correlations with building response over magnitude, distance, and site condition (e.g., _Vs30_). IM-EDP relationships have been explored previously. [PERSON] [3] coined the term \"efficiency\" to describe a given IM, whereby an efficient IM generates less variability (dispersion) about an estimated median in the predicted EDP. Efficiency is quantified by the standard deviation (\"sigma\") in a prescribed EDP-IM relationship (Equation (1)). [PERSON] et al. [4] used \"practicality\" as another descriptor of an IM to examine direct correlations between IM and EDP. In practice, it is measured using the slope (regression parameter \"b\" in Equation (1) below) of the predictive relationship between IM and EDP. If the slope approaches b = 0, there is smaller dependence of the EDP on the IM, indicating that the IM is less practical to be used for structural design purposes. [PERSON] et al. [4] also proposed \"proficiency\" as an indicator of IM, to investigate the combined effect of both efficiency and practicality. Proficiency is measured by a modified dispersion measure (\(\zeta=\frac{\sigma}{b}\)) that quantifies the uncertainty introduced in a regression model as shown in Equation (1),  
\[log\left(EDP\right)=a+b^{*}log\left(IM\right)+\delta \tag{1}\]  
Here, \(a\) and \(b\) are coefficients obtained through linear regression; \(\delta\) is the residual variability to characterize the variabilities between observed and predicted EDPs. For Equation (1), a lower dispersion measure \(\zeta\) indicates a more proficient IM. [PERSON] and [PERSON] [5] introduced the term \"sufficiency\" for IM-EDP relationships that are invariant over magnitude, fault mechanism, epicentral distance, and site class. More recently, [PERSON] et al. [6] proposed a \"steadfastness\" measure to determine the robustness of IMs with respect to variations in building properties.