  In the moduli space of degree d polynomials, we prove the equidistribution of
postcritically finite polynomials toward the bifurcation measure. More
precisely, using complex analytic arguments and pluripotential theory, we prove
the exponential speed of convergence for C 2-observables. This improves results
obtained with arithmetic methods by Favre and Rivera-Letellier in the
unicritical family and Favre and the first author in the space of degree d
polynomials. We deduce from that the equidistribution of hyperbolic parameters
with (d -- 1) distinct attracting cycles of given multipliers toward the
bifurcation measure with exponential speed for C 1-observables. As an
application, we prove the equidistribution (up to an explicit extraction) of
parameters with (d -- 1) distinct cycles with prescribed multiplier toward the
bifurcation measure for any (d -- 1) multipliers outside a pluripolar set.
