This work starts with PITT experimental data reported by Xia et al. from thin-film LiCoO2 electrodes prepared on a Si substrate by pulse laser deposition. In this article, we show that (i) the value of chemical diffusion coefficient of lithium-ion evaluated by graphical processing techniques is often erroneous, (ii) non-linear curve fitting is a better approach for accurate determination of thermodynamic, kinetic and diffusion parameters of ion-insertion electrodes from PITT data, (iii) the concept of anomalous diffusion can be applied to ion-insertion electrodes investigated by PITT, (iv) numerical inversion of Laplace transforms is a useful tool to derive the relevant model for representation of PITT data and (v) implementation of the whole calculation procedure becomes an easy task in the environment of Mathematica or other equivalent softwares.