The information geometry of the 2-manifold of gamma probability density functions provides a framework in which pseudorandom number generators may be evaluated using a neighbourhood of the curve of exponential density functions. The process is illust
rated using the pseudorandom number generator in Mathematica. This methodology may be useful to add to the current family of test procedures in real applications to finite sampling data.
Ambrose, Palais and Singer cite{Ambrose} introduced the concept of second order structures on finite dimensional manifolds. Kumar and Viswanath cite{Kumar} extended these results to the category of Banach manifolds. In the present paper all of these
results are generalized to a large class of Frechet manifolds. It is proved that the existence of Christoffel and Hessian structures, connections, sprays and dissections are equivalent on those Frechet manifolds which can be considered as projective limits of Banach manifolds. These concepts provide also an alternative way for the study of ordinary differential equations on non-Banach infinite dimensional manifolds. Concrete examples of the structures are provided using direct and flat connections.
