CONTINUED FRACTIONS ON REAL SYMMETRICAL MATRICES AND GAUSSIAN INVERSE-DISTRIBUTION

We consider a natural extension to the cone S(d) of (d, d) real symmetric positive definite matrices of the generalized inverse Gaussian distribution on the half positive real line. We characterize this distribution on S(d) in the G. Letac and V. Seshadri's manner [4] by replacing the gamma hy the Wishart distributions and by using the generalization to S(d) of real continued fractions. For this we use real Lagrangians.