  This paper is mainly dedicated to an extension of the Slepian-Bangs formula
to non-circular complex elliptical symmetric (NC-CES) distributions, which is
derived from a new stochastic representation theorem. This formula includes the
non-circular complex Gaussian and the circular CES (CCES) distributions. Some
general relations between the Cramer Rao bound (CRB) under CES and Gaussian
distributions are deduced. It is proved in particular that the Gaussian
distribution does not always lead to the largest stochastic CRB (SCRB) as many
authors tend to believe it. Finally a particular attention is paid to the noisy
mixture where closedform expressions for the SCRBs of the parameters of
interest are derived.
