  This paper presents an in-depth study of how to estimate the sensitivity of
searches for gravitational-wave pulsars -- rapidly-rotating neutron stars which
emit quasi-sinusoidal gravitational waves. It is particularly concerned with
searches over a wide range of possible source parameters, such as searches over
the entire sky and broad frequency bands. Traditional approaches to estimating
the sensitivity of such searches use either computationally-expensive Monte
Carlo simulations, or analytic methods which sacrifice accuracy by making an
unphysical assumption about the population of sources being searched for. This
paper develops a new, analytic method of estimating search sensitivity which
does not rely upon this unphysical assumption. Unlike previous analytic
methods, the new method accurately predicts the sensitivity obtained using
Monte Carlo simulations, while avoiding their computational expense. The change
in estimated sensitivity due to properties of the search template bank, and the
geographic configuration of the gravitational wave detector network, are also
investigated.
