  Distributions of wave characteristics of ocean waves, such as wave slope,
waveheight or wavelength, are an important tool in a variety of oceanographic
applications such as safety of ocean structures or in the study of ship
stability, as will be the focus in this paper. We derive Palm distributions of
several wave characteristics that can be related to steepness of waves for two
different cases, namely for waves observed along a line at a fixed time point
and for waves encountering a ship sailing on the ocean. The relation between
the distributions obtained in the two cases is also given physical
interpretation in terms of a ``Doppler shift'' that is related to the velocity
of the ship and the velocities of the individual waves.
