  A weak measurement consists in coupling a system to a probe in such a way
that constructive interference generates a large output. So far, only the
average output of the probe and its variance were studied. Here, the
characteristic function for the moments of the output is provided. The outputs
considered are not limited to the eigenstates of the pointer or of its
conjugate variable, so that the results apply to any observable $\Hat{o}$ of
the probe. Furthermore, a family of well behaved complex quantities, the normal
weak values, is introduced, in terms of which the statistics of the weak
measurement can be described. It is shown that, within a good approximation,
the whole statistics of weak measurement is described by a complex parameter,
the weak value, and a real one.
