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This paper statistically describes the orbital distribution laws of Jupiter'sirregular moons, most of which are members of the Ananke, Carme and Pasiphaegroups. By comparing 19 known continuous distributions, it is verified thatsuitable distribution functions exist to describe the orbital distributions ofthese natural satellites. For each distribution type, interval estimation isused to estimate the corresponding parameter values. At a given significancelevel, a one-sample Kolmogorov-Smirnov non-parametric test is applied to verifythe specified distribution, and we often select the one with the largest$p$-value. The results show that the semi-major axis, mean inclination andorbital period of the moons in the Ananke group and Carme group obey Stabledistributions. In addition, according to Kepler's third law of planetary motionand by comparing the theoretically calculated best-fitting cumulativedistribution function (CDF) with the observed CDF, we demonstrate that thetheoretical distribution is in good agreement with the empirical distribution.Therefore, these characteristics of Jupiter's irregular moons are indeed verylikely to follow some specific distribution laws, and it will be possible touse these laws to help study certain features of poorly investigated moons oreven predict undiscovered ones.

Revisiting the distributions of Jupiter's irregular moons: II. orbital characteristics