  This paper statistically describes the orbital distribution laws of Jupiter's
irregular moons, most of which are members of the Ananke, Carme and Pasiphae
groups. By comparing 19 known continuous distributions, it is verified that
suitable distribution functions exist to describe the orbital distributions of
these natural satellites. For each distribution type, interval estimation is
used to estimate the corresponding parameter values. At a given significance
level, a one-sample Kolmogorov-Smirnov non-parametric test is applied to verify
the specified distribution, and we often select the one with the largest
$p$-value. The results show that the semi-major axis, mean inclination and
orbital period of the moons in the Ananke group and Carme group obey Stable
distributions. In addition, according to Kepler's third law of planetary motion
and by comparing the theoretically calculated best-fitting cumulative
distribution function (CDF) with the observed CDF, we demonstrate that the
theoretical distribution is in good agreement with the empirical distribution.
Therefore, these characteristics of Jupiter's irregular moons are indeed very
likely to follow some specific distribution laws, and it will be possible to
use these laws to help study certain features of poorly investigated moons or
even predict undiscovered ones.
