  In this paper, we introduce a complete family of parametrized
quasi-probability distributions in phase space and their corresponding Weyl
quantization maps with the aim to generalize the recently developed Wigner-Weyl
formalism within the Loop Quantum Cosmology program (LQC). In particular, we
intend to define those quasi-distributions for states valued on the Bohr
compactification of the real line in such a way that they are labeled by a
parameter that accounts for the ordering ambiguity corresponding to
non-commutative quantum operators. Hence, we notice that the projections of the
parametrized quasi-probability distributions result in marginal probability
densities which are invariant under any ordering prescription. We also note
that, in opposition to the standard Schr\"odinger representation, for an
arbitrary character the quasi-distributions determine a positive function
independently of the ordering. Further, by judiciously implementing a
parametric-ordered Weyl quantization map for LQG, we are able to recover in a
simple manner the relevant cases of the standard, anti-standard, and Weyl
symmetric orderings, respectively. We expect that our results may serve to
analyze several fundamental aspects within the LQC program, in special those
related to coherence, squeezed states, and the convergence of operators, as
extensively analyzed in the quantum optics and in the quantum information
frameworks.
