Dual Geometric Structures and Instability of Bivariate Weibull Statistical Manifold

To investigate the stability of bivariate Weibull distribution from the viewpoint of information geometry,the set of all bivariate Weibull distributions was considered as a manifold which was called bivariate Weibull statistical manifold. By computing the Fisher information matrix,the α-connections,α-curvature tensors,α-scalar curvature,and dual geometric structures were obtained. Moreover,bivariate Weibull statistical manifold was dual flat and had constant sectional curvature for α=± 1. Meanwhile,in virtue of the dual flat geometric structures,the instability of the geodesic spreads on this manifold was obtained via the divergence(or instability) of the Jacobi vector field.