  We analyse the statistical distribution function for the height fluctuations
of brittle fracture surfaces using extensive experimental data sampled on
widely different materials and geometries. We compare a direct measurement of
the distribution to a new analysis based on the structure functions. For length
scales $\delta$ larger than a characteristic scale $\delta^*$, we find that the
distribution of the height increments $\Delta h = h(x+ \delta) -h(x)$ is
Gaussian. Self-affinity enters through the scaling of the standard deviation
$\sigma$, which is proportional to $\delta^\zeta$ with a unique roughness
exponent. Below the scale $\delta^*$ we observe an effective multi-affine
behavior of the height fluctuations and a deviation from a Gaussian
distribution which is related to the discreteness of the measurement or of the
material.
