  By introducing a second complex variable, the integral relation between a
complex density and the corresponding positive distribution is derived.
Together with the positivity and normalizability conditions, this sum rule
allows to construct explicitly equivalent pairs of distributions in simple
cases discussed here. In particular the well known solution for a complex
gaussian distribution is generalized to an arbitrary complex inverse dispersion
parameter. This opens a possibility of positive representation of Feynman path
integrals directly in the Minkowski time.
