Stochastic Assessment of Acceleration Probability Density Function for Parametric Rolling Using Moment Method

The paper correctly states the linearity-based moment decompositions for roll angular acceleration and cargo lateral acceleration and proposes two parametric PDF families, but it omits necessary hypotheses (e.g., symmetry conditions) when dropping cross-terms in E[K1^2], gives no normalization constants or existence/uniqueness proofs for the proposed PDFs, and does not derive first-order conditions for the moment-matching objective. The model solution supplies these missing pieces (moment expansions including the cross-terms, normalizers for both families, dominated-convergence justifications, covariance-form gradient conditions, and exact variance for the logistic case). Aside from a minor, easily corrected circularity in one sub-step of the even-quartic parameterization, the model solution is sound.