Randomly generated distributions

A new scheme for randomly generating probability distributions on the interval 0, 1] is introduced. The scheme can also be viewed as a way to generate homeomorphisms at random. Conditions are given so that a continuous measure with full support is generated almost surely. Geometric properties of the generated probability measures are examined, including the dimension and derivative structure of the measures and their respective distribution functions. For example, we give conditions so that almost all the distribution functions of the measures generated are strictly singular. Applications include determining average case errors for numerical methods of equation solving and Bayesian statistics. Research supported by NSF Grant DMS-9303888.