  We attempt to construct the exact univariate probability distributions for 2
x 2 quantum systems that yield the (balanced) univariate Hilbert-Schmidt
determinantal moments <(|rho| |rho^{PT}|)^n>, obtained by Slater and Dunkl (J.
Phys. A, 45, 095305 [2012]). To begin, we follow--to the extent possible--the
Mellin transform-based approach of Penson and Zyczkowski in their study of
Fuss-Catalan and Raney distributions (Phys. Rev. E, 83, 061118 [2011]).
Further, we approximate the y-intercepts (separability/entanglement
boundaries)--at which |rho^{PT}|=0-- of the associated probability
distributions based on the (balanced) moments, as well as the previously
reported unbalanced determinantal moments <|rho^{PT}|^n>, as a function of the
seventy-two values of the Dyson-index-like parameter alpha = 1/2 (rebits), 1
(qubits),...,2 (quaterbits),...35.
