A joint probability density is derived for wavelengths and wave heights. It
is asymmetric and depends only on the spectral bandwidth epsilon defined b
y Cartwright and Longuet-Higgins (1956). After that a theoretical probabili
ty density for wave steepness is obtained. It tends to Rayleigh distributio
n as epsilon --> 0. A comparison between theoretical steepness distribution
and laboratory experiment result shows good agreement.