  We propose a new formulation of the probability distribution function of wind
driven water surface slope with an $\alpha$-stable distribution probability.
The mathematical formulation of the probability distribution function is given
under an integral formulation. Application to represent the probability of time
slope data from laboratory experiments is carried out with satisfactory
results. We compare also the $\alpha$-stable model of the water surface slopes
with the Gram-Charlier development and the non-Gaussian model of Liu et
al\cite{Liu}. Discussions and conclusions are conducted on the basis of the
data fit results and the model analysis comparison.
