We report a study of simple ABO₃ type perovskites BaTiO₃, PbTiO₃, KNbO₃, SrTiO₃ and the relaxor perovskites PbSc_1/2Nb_1/2O₃ (PSN) in their cubic phase using hard synchrotron radiation and hot neutrons. Gram-Charlier expansions of the thermal parameters have been performed and have revealed interesting features about the probability density function and the one-particle potential of the different atoms. This description is compared with other descriptions in terms of the split atom model and in terms of the rotator model. Structural trends regarding the order-disorder versus displacive character of the phase transitions have been obtained. It is concluded that SrTiO₃ and BaTiO₃ are quasi-harmonic systems whereas KNbO₃ shows weak anharmonicity and PbTiO₃ and PSN display strong anharmonic features.