Lagrangian Function on the Finite State Space Statistical Bundle

The statistical bundle is the set of couples (Q, W) of a probability density Q and a random 1 variable W such that EQ [W] = 0. On a finite state space, we assume Q to be a probability density with 2 respect to the uniform probability and give an affine atlas of charts such that the resulting manifold is 3 a model for Information Geometry. Velocity and accelleration of a one-dimensional statistical model 4 are computed in this set up. The Euler-Lagrange equations are derived from the Lagrange action 5 integral. An example of Lagrangian using minus the entropy as potential energy is briefly discussed. 6