  A method is suggested to decompose the statistical and systematic
uncertainties from the residues between the calculation of a theoretical model
and the observed data. The residues and the parameters of the model can be
obtained through the standard statistical fitting procedures. The present work
concentrates on the decomposition of the total uncertainty, of which the
distribution corresponds to that of the residues. The distribution of the total
uncertainty is considered as two normal distributions, statistical and
systematic uncertainties. The standard deviation of the statistical part,
{\sigma}stat, is estimated through random parameters distributed around their
best fitted values. The two normal distributions are obtained by minimizing the
moments of the distribution of the residues with the fixed {\sigma}stat. The
method is applied to the liquid drop model (LD). The statistical and systematic
uncertainties are decomposed from the residues of the nuclear binding energies
with and without the consideration of the shell effect in LD. The estimated
distributions of the statistical and systematic uncertainties can well describe
that of the residues. The normal assumption of the distribution of the
statistical and systematic uncertainties is examined through various
approaches. The comparison between the distributions of the specific nuclei and
those of the statistical and systematic uncertainties are consistent with the
physical considerations, although the latter two can be obtained without the
knowledge of these considerations. Such as, the LD are more suitable to
describe the heavy nuclei. The light and heavy nuclei are indeed distributed
mostly inside the distributions of the statistical and systematic
uncertainties, respectively. The similar situation are also found for the
nuclei close to and far from shell. The present method is also performed to
nuclei around stability line.
