  Probability distributions and densities are derived for the excess and
deficiency of the intensity or instantaneous energy (quasi-static power)
associated with a $p$-dimensional random vector field. Explicit expressions for
the exact distributions are obtained for arbitrary threshold levels, together
with simple approximate functions for relatively high or low thresholds. It is
shown that precise expressions only require an expansion of order $p-1$ in the
ratio of the excess height to the threshold level. Numerical simulations
validate the analytical results.
