  We derive a Bell inequality based on a generalized quasiprobability function
which is parameterized by one non-positive real value. Two types of known Bell
inequalities formulated in terms of the Wigner and Q functions are included as
limiting cases. We investigate violations of our Bell inequalities for single
photon entangled states and two-mode squeezed vacuum states when varying the
detector efficiency. We show that the Bell inequality for the Q function allows
the lowest detection efficiency for violations of local realism.
