It is obvious that the 3pF function gives higher accuracy than 2pF function for the five nuclides presented in Table 1. For 60Ni and 208Pb, the improvement is slight compared to the improvement for the other nuclides. For 60Ni, the RSS decreases only by 2 % of its value when the depression parameter is considered. In other words, the fitted 2pF and 3pF distributions are almost identical for 60Ni charge density. For 152Sm, the RSS decreases by about 75% when the depression parameter is considered, this implies that the use of 3pF provides significant improvement in the quality of the fit. The fitting of model-independent density to d3pF distribution provides a great improvement over the other two formulas. For 40Ca, 60Ni and 100Mo, the RSS corresponding to d3pF distribution is less than 1 % of its values in the case of 2pF. For 152Sm and 208Pb, RSS is about 1.8 % and 4.4 % , respectively, of the corresponding values in the case of 2pF.
It should be noted that the three formulas studied in this paper provide reasonable approximation of the charge, proton and neutron densities. From the statistical point of view, the fitting is improved as the number of adjustable parameters increase, but one should be careful when talking about the significance of improvement. For a calculation which is sensitive to the fine details of density the improvement would be very significant. But for a calculation which deals only with the tail of density distribution, or the fine details of core density does not affect the result, the improvement would be insignificant. It is expected that consideration of d3pF distribution would improve the calculation of nuclear structure and decay. In contrast, no significant improvement is expected for nuclear reactions and scattering calculation. Anyway, the improvement in the deferent types of calculations should be studied carefully in a separate study.