Experimental collisional energy transfer data from kinetically controlled selective ionization (KCSI) and ultraviolet absorption (UVA) experiments are analyzed in the framework of the partially ergodic collision theory (PECT). Collisions of azulene and biphenylene with different colliders are investigated as case studies. The downward wings of the P(E',E) energy transfer distributions obtained from the PECT model are fitted to the recently introduced "variable-shape"-exponential 3-parameter functional form of P(E,E) obtained from KCSI experiments, P(E',E) ∝ exp[-{(E - E')/(C-0 + C1E)}(Y)]. The PECT model is able to reproduce the characteristic dependence of the KCSI "shape parameter" Y on the choice of collider, the energy dependent width of the KCSI P(E',E) distributions, described by (α(E) = C-0 + C1E, and the temperature dependence of the UVA data above room temperature. The statistical approach of PECT obviously captures the essence of large molecule energy transfer at chemically significant energies without the need of knowing specific features of the detailed collision dynamics. It therefore shows promise for predicting the shape of P(E,E) in master equation kernels for larger molecules.