  We present an analytical derivation of the switching field distribution for a
single domain particle from the N\'eel-Brown model in the presence of a
linearly swept magnetic field and influenced by thermal fluctuations. We show
that the switching field distribution corresponds to a probability density
function and can be obtained by solving a master equation for the not-switching
probability together with the transition rate for the magnetization according
to the Arrhenius-N\'eel Law. By calculating the first and second moments of the
probability density function we succeed in modeling rate-dependent coercivity
and the standard deviation of the coercive field. Complementary to the
analytical approach, we also present a Monte Carlo simulation for the switching
of a macrospin, which allows us to account for the field dependence of the
attempt frequency. The results show excellent agreement with results from a
Langevin dynamics simulation and therefore point out the importance to include
the relevant dependencies in the attempt frequency. However, we conclude that
the N\'eel-Brown model fails to predict switching fields correctly for common
field rates and material parameters used in magnetic recording from the loss of
normalization of the probability density function. Investigating the transition
regime between thermally assisted and dynamic switching will be of future
interest regarding the development of new magnetic recording technologies.
