  We present a new approach for obtaining quantum quasi-probability
distributions, $P(\alpha,\beta)$, for two arbitrary operators, $\mathbf{a}$ and
$\mathbf{b}$, where $\alpha$ and $\beta$ are the corresponding c-variables. We
show that the quantum expectation value of an arbitrary operator can always be
expressed as a phase space integral over $\alpha$ and $\beta$, where the
integrand is a product of two terms: One dependent only on the quantum state,
and the other only on the operator. In this formulation, the concepts of
quasi-probability and correspondence rule arise naturally in that
simultaneously with the derivation of the quasi-distribution, one obtains the
generalization of the concept of correspondence rule for arbitrary operators.
