The large scale distribution of matter in the universe contains valuable information about fundamental cosmological parameters and the properties of dark matter. Unfortunately much of the important information lies on scales below which nonlinear gravitational effects have taken hold, complicating both models and statistics considerably. This thesis deals with the distribution of matter - mass and galaxies - on such scales. The aim is to develop new statistical tools that make use of nonlinear evolution for the purposes of constraining cosmological models. A new derivation for the 1-point probability distribution function (PDF) for density inhomogeneities is presented first. The calculation makes use of the Chapman-Kolmogorov equation and second order Eulerian perturbation theory to propagate the initial density field into the nonlinear regime. The analysis is extended to give the 1-point PDF of galaxies in redshift space. The effect of nonlinear and stochastic biasing is considered and a new result for the skewness in redshift space is found. Finally an extension of the Gaussian likelihood analysis method for non-Gaussian fields is presented. Concentrating on non-Gaussianity due to nonlinear evolution under gravity, a generalised Fisher analysis is applied to a model of a Galaxy redshift survey, including the effects of biasing, redshift space distortions and shot noise. The results indicate that using nonlinear likelihood analysis may yield marginalised parameter uncertainties around the few percent level from forthcoming large galaxy redshift surveys.