Gaussian distributions, Jacobi group, and Siegel-Jacobi space
Gaussian distributions, Jacobi group, and Siegel-Jacobi space
Let N be the space of Gaussian distribution functions over ℝ, regarded as a 2-dimensional statistical manifold parameterized by the mean μ and the deviation σ. In this paper, we show that the tangent bundle of N, endowed with its natural Kähler structure, is the Siegel-Jacobi space appearing in the …