Distributions of ψ (beam orientation) and ε (inverse Doppler factor) for the Crab, Vela, and Dragonfly pulsars. Each column corresponds to one pulsar, with the top row showing the orientation-angle distribution ψ and the bottom row showing the Doppler parameter ε. Both quantities are energy independent and were derived from the same four-beam fits used in Table 1. The colors and the dotted line style have the same meanings as in Figure 1.