Composite biased pdf (top row) and corresponding weight factor (bottom row) for path length stretching. The first and second columns correspond to the path length stretching for two different optical depths along the path (τ_path = 5 and 20 respectively). The third and fourth columns correspond to the same cases, but now path length stretching is combined with forced interaction. Within each panel, the different lines correspond to different values of the mixing parameter ξ, ranging from ξ = 0 (no biasing) to ξ = 1 (pure biasing, no composite biasing).