Upper panel: Probability distribution function (PDF) of the projected offset between the BCG position and the weak-lensing-determined halo center. Red data points show the observed BCG offsets in our sample, with error bars estimated via 1000 bootstrap resamplings. The solid blue and black lines represent the best-fitting single- and two-component 2D Gaussian models, respectively. The dashed purple and orange lines correspond to the well-centered and miscentered components of the two-component model. All offset scale parameters, including σ, σ₁, and σ₂, are expressed in units of h⁻¹ kpc. Lower panels: Fitting results for the two-component (left) and single-component (right) 2D Gaussian models. Contours indicate 1σ and 2σ confidence levels, with best-fitting values and 68% confidence intervals shown above each 1D marginalized distribution.