  A number of recent studies have estimated the inter-galactic void probability
function and investigated its departure from various random models. We study a
family of parametric statistical models based on gamma distributions, which do
give realistic descriptions for other stochastic porous media. Gamma
distributions contain as a special case the exponential distributions, which
correspond to the `random' void size probability arising from Poisson
processes. The random case corresponds to the information-theoretic maximum
entropy or maximum uncertainty model. Lower entropy models correspond on the
one hand to more `clustered' structures or `more dispersed' structures than
expected at random. The space of parameters is a surface with a natural
Riemannian structure, the Fisher information metric. This surface contains the
Poisson processes as an isometric embedding and provides the geometric setting
for quantifying departures from randomness and perhaps on which may be written
evolutionary dynamics for the void size distribution. Estimates are obtained
for the two parameters of the void diameter distribution for an illustrative
example of data published by Fairall.
